Quadratic Equation: Class10

Q1.If one root of the quadratic equation 6x² − 𝑥 − 𝑘 = 0 is 2/3 , then find the value of 𝑘.

2/3

3

2

1/3

Q2. Find the value of 𝑘, for which one root of the quadratic equation 𝑘x² − 14𝑥 + 8 = 0 is six times the other

3 ohm

5 ohm

5/6 ohm

-2/3 ohm

Q3. If 𝑥 = (−1/2), is a solution of the quadratic equation 3x² + 2𝑘𝑥 − 3 = 0, find the value of k?

2/3

3/5

9/4

None

Q4.If the quadratic equation 𝑝x² − 2√5 𝑝𝑥 + 15 = 0 has two equal roots, then find the value of P?

2/3

3

3/2

-1/2

Q5.If 1 is a root of the equations 𝑎y² + 𝑎𝑦 + 3 = 0 and 𝑦^2 + 𝑦 + 𝑏 = 0, then 𝑎𝑏 equals:

3

-3

1/3

None of the above

Q6.If the quadratic equation 𝑚x² + 2𝑥 + 𝑚 = 0 has two equal roots, then the values of 𝑚 are

±2

±1

±1/3

None of these

Q7.The roots of the equation x² + 𝑥 − 𝑝(𝑝 + 1) = 0, where 𝑝 is a constant, are

−p,−(p+1)

p,−(p+1)

−p,(p+1)

None of these

Q8. What is the nature of roots of the quadratic equation 4x² −12𝑥 − 9 = 0?

only one real root

two complex roots.

two real and distinct roots

None of these

Q9.For what value of 𝑘 the quadratic equation x² − 𝑘𝑥 + 4 = 0 has equal roots?

±1

±2

±3

±4

Q10. Which of the following is not a quadratic equation.

x² + 3x – 5 = 0

x² + x³ – 5 = 0

3 + x + x² = 0

x² – 9 = 0

Q11. The quadratic equation has degree

0

1

2

3

Q12.The polynomial equation x (x + 1) + 8 = (x + 2) (x – 2) is

linear equation

quadretic equation

cubic equation

None of these

Q13. The quadratic equation whose roots are 1 is

2x² + x – 1 = 0

2x² – x – 1 = 0

2x² + x + 1 = 0

2x² – x + 1 = 0

Q14. The sum of the roots of the quadratic equation 3x² – 9x + 5 = 0 is

3

6

-3

2

Q15. If the roots of ax² + bx + c = 0 are in the ratio m : n, then

mna² = (m + n) c

mnb² = (m + n) ac

mn b² = (m + n)² ac

mnb² = (m – n)² ac

Q16. If the roots of px² + qx + 2 = 0 are reciprocal of each other, then

P = 0

p = -2

p = ±2

p = 2

Q17. The equation 12x² + 4kx + 3 = 0 has real and equal roots, if

k = ±3

k = ±4

k = ±2

k = ±1

Q18. Roots of a quadratic equation are imaginary when discriminant is ______________

zero

less to zero

more than zero

None of the above

Q19.The sum of the squares of two consecutive natural numbers is 313. The numbers are

13,14

12,13

13,15

none of the above

Q20.The roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then

2a = b + c

2c = a + b

b = a + c

2b = a + c