Advertisements
Advertisements
प्रश्न
Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
Advertisements
उत्तर
Solution:
Given: Quadratic equation 9x2-3kx + k = 0 has equal roots
Let β be the equal roots of the equation
Thus 2β =(3k)/9=k/3 (Sum of the roots is equal to –b/a)
We get β=k/6 or β2=k2/36
Also that β2=k/9 (Product of the roots is equal to c/a)
k2/36=k/9
For k ≠ 0,k/36=1/9
thus k=4
APPEARS IN
संबंधित प्रश्न
Find that value of p for which the quadratic equation (p + 1)x2 – 6(p + 1)x + 3(p + 9) = 0, p ≠ –1 has equal roots. Hence, find the roots of the equation.
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
kx2 + 2x + 3k = 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
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
The quadratic equation whose roots are 1:
If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then:
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
