Advertisements
Advertisements
Question
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Advertisements
Solution
-5 is a root of the quadratic equation
2x2 + px – 15 = 0, then
⇒ 2(5)2 – p( -5) – 15 = 0
⇒ 50 – 5p – 15 = 0
⇒ 35 – 5p = 0
⇒ 5p = 35 = 0
⇒ p = `(35)/(5)` = 7
p(x2 + x) + k = 0 has equal roots
⇒ px2 + px + k = 0
⇒ 7x2 + 7x + k = 0
Here, a = 7, b = 7, c = k
b2 - 4ac
= (7)2 - 4 x 7 x k
= 49 - 28k
∵ Roots are equal
∴ b2 - 4ac = 0
⇒ 49 - 28k = 0
⇒ 28k = 49
⇒ k = `(49)/(28) = (7)/(4)`
∴ k = `(7)/(4)`.
APPEARS IN
RELATED QUESTIONS
For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Solve the following quadratic equation using formula method only
25x2 + 30x + 7 = 0
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
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:
2x2 - (3k + 1)x - k + 7 = 0.
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
