Question

If-5 is a root of the quadratic equation 2x + px -15 = 0 and the quadratic equation

px + x+ k = 0 has equal roots, find the value of k.

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Given

x = -5

Putting x in the polynomial

2x² + px - 15 = 0

=> 2(-5)² + p(-5) - 15 = 0

=> 50 - 5p - 15 = 0

=> 5p = 35

=> p = 7

If, px² + x+ k has equal roots

Discriminant, D = 0

OR => b² - 4ac = 0

Comparing with the form ax² + bx + c

we have: a = p = 7 ; b = 1, c = k

So, b² - 4ac = 0

=> (1)² - 4(p)(k) = 0

=> 1 - 4(7)k = 0

=> 1 - 28k = 0

=> k = 1/28