

SAT Mathematics - Quadratic Equation
Exam Duration: 45 Mins Total Questions : 30
The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is
- (a)
\(\frac { 1 }{ 289 } \)
- (b)
\(\frac { 289 }{ 290 } \)
- (c)
\(\frac { 290 }{ 289 } \)
- (d)
289
If, \(x+\frac { 1 }{ x } =3\) then the value of x6+\(\frac { 1 }{ { x }^{ 6 } } \) is
- (a)
927
- (b)
114
- (c)
364
- (d)
322
ax2+bx+c=0, where a,b and c are real roots, if
- (a)
c = 0
- (b)
b2>3ac
- (c)
a, b, c are integers
- (d)
ac>0, and b is zero
The number of real roots of quadratic equation x2-3|x|-10 = 0 is
- (a)
1
- (b)
2
- (c)
3
- (d)
4
If one root of the two quadratic equations x2+ax+b=0 and x2+bx+a=0 is common, then
- (a)
a + b = 1
- (b)
a + b = -1
- (c)
ab = 1
- (d)
ab = -1
If the equation x2 - kx + 1 = 0, has no real roots then
- (a)
-2<k<2
- (b)
-3<k<3
- (c)
-4<k<4
- (d)
none of these
If \(\alpha\) and \(\beta\) are the roots of quadratic equation x2-2x+1, then \(\alpha\)2+\(\beta\)2 is
- (a)
1
- (b)
3
- (c)
2
- (d)
-2
Find the nature of the roots of the quadratic equation \({ 3x }^{ 2 }-4\sqrt { 3 } x+4=0\)
- (a)
\(2\frac { \sqrt { 3 } }{ 3 } ,2\frac { \sqrt { 3 } }{ 3 } \)
- (b)
\(2\frac { \sqrt { 3 } }{ \sqrt { 3 } } ,2\frac { \sqrt { 3 } }{ \sqrt { 3 } } \)
- (c)
\(2\frac { \sqrt { 3 } }{ 3 } ,-2\frac { \sqrt { 3 } }{ 3 } \)
- (d)
None of these
Solve 5(x+1) + 5(2-x) = 53+1
- (a)
2, -1
- (b)
-2, 1
- (c)
-2, -1
- (d)
None of these
A total number of 324 coins of 20 paise and 25 paise makes a sum of Rs 71. The number of 25 paise coins
- (a)
120
- (b)
124
- (c)
37
- (d)
40
If the root of the equation (b-c)x2 + (c-a)x+(a-b) = 0 is 1, the other root will be
- (a)
1
- (b)
\(\frac { b-a }{ b-c } \)
- (c)
\(\frac { a-b }{ b-c } \)
- (d)
None of these
If \(\alpha\) and \(\beta\) are roots of the equation x2-k(x+1)-c=0, the values of (\(\alpha\)+1)(\(\beta\)+1) is equal to
- (a)
1
- (b)
1-c
- (c)
0
- (d)
None of these
The value of m for which the equation 3x2+(7+m) x+2-m=0 has equal roots is
- (a)
-1
- (b)
1
- (c)
25
- (d)
None of these
The nature of the roots of the quadratic equation a2b2y2 + 2abcy +c2 = 0,
- (a)
Real and equal
- (b)
Real and Distinct
- (c)
No real roots
- (d)
Reciprocal roots
The roots of the quadratic equation are (b+a)x2-2(b2-a2)x+(b-a)2 = 0 are
- (a)
Equal
- (b)
Distinct
- (c)
Real
- (d)
None
The roots of the quadratic equation x2-x-12=0 are
- (a)
4,-3
- (b)
-4, 3
- (c)
-4, -3
- (d)
None of these
Sashankand Manav together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Represent this situation in the form of a quadratic equation
- (a)
(x-5)(40-x) = 124
- (b)
(x-5)(x-40) = 124
- (c)
(5+x)(40-x) = 124
- (d)
None of these
The sum of a number and its reciprocal is \(\frac { 5 }{ 2 } \). Represent this situation in the form of a quadratic equation
- (a)
\(x+\frac { 1 }{ x } =\frac { 5 }{ 2 } \)
- (b)
\(x-\frac { 1 }{ x } =\frac { 5 }{ 2 } \)
- (c)
\({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } =\frac { 5 }{ 2 } \)
- (d)
\(x+\sqrt { x } =\frac { 5 }{ 2 } \)
The quadratic equation has two distinct roots if
- (a)
b2 = 4ac
- (b)
b2>4ac
- (c)
b2<4ac
- (d)
b2 = ac
The discriminant of the quadratic equation 2x2-4x+3 = 0 is
- (a)
8
- (b)
-8
- (c)
4
- (d)
-4
The roots of the quadratic equation 2x2-4x + 3 are
- (a)
Real and distinct
- (b)
Real and equal
- (c)
No real roots
- (d)
Reciprocal roots
Find the value of k if the roots of the quadratic equation kx(x-2) +6=0 are equal
- (a)
3
- (b)
4
- (c)
5
- (d)
6
If the sum of the roots of the quadratic equation 3x2+(2k+1)x-(k+5)=0 is equal to the product of the roots, then the value of k is
- (a)
2
- (b)
3
- (c)
4
- (d)
5
If the two roots of the two quadratic equations x2 + mx + 1 = 0 and ax2 + bx + \(\alpha\) = 0 are common, then the value of m is
- (a)
ab
- (b)
b
- (c)
\(\frac { a }{ b } \)
- (d)
\(\frac { b }{ a } \)
The condition that both the roots of the two quadratic equation a1x2+b1x+c1=0 and a2x2+b2x+c2=0 are common is
- (a)
a1a2|b1b2+c1c2=0
- (b)
\(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } =\frac { { c }_{ 1 } }{ { c }_{ 2 } } \)
- (c)
\({ a }_{ 1 }+{ b }_{ 1 }+{ c }_{ 1 }={ a }_{ 2 }+{ b }_{ 2 }+{ c }_{ 2 }\frac { W }{ R } \)
- (d)
\({ a }_{ 1 }^{ 2 }+{ b }_{ 1 }^{ 2 }+{ c }_{ 1 }^{ 2 }={ a }_{ 2 }^{ 2 }+{ b }_{ 2 }^{ 2 }+{ c }_{ 2 }^{ 2 }\)
The product of two consecutive natural numbers is 72, Find the natural numbers.
- (a)
8, 9
- (b)
6, 12
- (c)
24, 3
- (d)
36, 2
If the difference of the roots of the quadratic equations x2-ax+b is 1, then
- (a)
a2-4b = 0
- (b)
a2-4b = -1
- (c)
a2-4b = 1
- (d)
a2-4b = 4
The roots of the quadratic equation (x-12) (2x+25)=0 are
- (a)
\(-12,\frac { -25 }{ 2 } \)
- (b)
\(12,\frac { -25 }{ 2 } \)
- (c)
\(-12,\frac { 25 }{ 2 } \)
- (d)
\(12,\frac { 25 }{ 2 } \)
The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number?
- (a)
7
- (b)
9
- (c)
11
- (d)
none
If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the number is:
- (a)
40
- (b)
44
- (c)
80
- (d)
88