Advertisements
Advertisements
प्रश्न
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Advertisements
उत्तर
The given quadratic equation is 3x2 − 2kx + 12 = 0
On comparing it with the general quadratic equation ax2 + b x + c = 0, we obtain
a = 3, b = −2k and c = 12
Discriminant, ‘D’ of the given quadratic equation is given by
D = b2 − 4ac
= (− 2k)2 − 4 × 3 × 12
= 4k2 − 144
For equal roots of the given quadratic equations, Discriminant will be equal to 0.
i.e., D = 0
`rArr 4k^2-144=0`
`rArr4(k^2-36)=0`
`rArrk^2=36`
`rArrk=+-6`
Thus, the values of k for which the quadratic equation 3x2 − 2kx + 12 = 0 will have equal roots are 6 and −6.
APPEARS IN
संबंधित प्रश्न
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − k = 0
If x = −2 is a root of the equation 3x2 + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x2 + k(4x + k − 1) + p = 0 are equal.
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.
If the ratio of the roots of the equation
lx2 + nx + n = 0 is p: q, Prove that
`sqrt(p/q) + sqrt(q/p) + sqrt(n/l) = 0.`
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0
If α, β are roots of the equation x2 + 5x + 5 = 0, then equation whose roots are α + 1 and β + 1 is:
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
