### Scholastic Aptitude Test - Mathematics - Quadratic Equation

#### Question - 1

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

#### Question - 2

If, $x+\frac { 1 }{ x } =3$ then the value of x6+$\frac { 1 }{ { x }^{ 6 } }$ is

• A 927
• B 114
• C 364
• D 322

#### Question - 3

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

#### Question - 4

The number of real roots of quadratic equation x2-3|x|-10 = 0 is

• A 1
• B 2
• C 3
• D 4

#### Question - 5

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

#### Question - 6

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

#### Question - 7

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

#### Question - 8

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

#### Question - 9

Solve 5(x+1) + 5(2-x) = 53+1

• A 2, -1
• B -2, 1
• C -2, -1
• D None of these

#### Question - 10

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