Question

If -4is aroot of quadratic equation 2xsquare +px-15 and quadratic equation p(xsquare+x)+k=0 has eaual roots,find the value of k

Answer 1

Proper Question :

If -4 is a root of Quadratic Equation 2x² +px-15 and quadratic equation p(x²+x)+k=0 has equal roots,find the value of k ?



✒ Solution :


✏ Theory : In this Question, It is Given that If -4 is a root of Quadratic Equation 2x² +px-15.

Quadratic Equation : 2x² + Px -15 = 0

✏ Putting X = (-4),


✏ 2x² + PX -15 = 0

✏ 2(-4)² + P(-4) - 15 = 0

✏ 2(16) -4P - 15 = 0

✏ 32 -15 - 4P = 0

✏ 17 -4P = 0

✏ 17 = 4p

✒ P = 4/17 ------(1)


Now, According to the Question!

Statement : We have Need to Find the Value of k ?


✒ Given :

✏ Equation : P(x² + x + k ) = 0

{ Putting X = -4 and P = 4/17 }


✏ P(x² + x + k ) = 0

✏ 4/17 {(-4)² + (-4) + k = 0

✏ 4/17 {(16-4+k)} = 0

✏ 4/17 {(12 + k )} = 0

✏ 4(12+k) = 0 × 17

✏ 48 + k = 0

✏ k = -48

Hence, Value of k is (-48).