if x is = -2 is a root of the equation 3x2 +7x +p =0 find the values - Maths - Quadratic Equations

Question

if x is = -2 is a root of the equation 3x2 +7x +p =0
find the values of k so that the roots of the equation
x2 +k (4x+k-1)+p=0 are equal
solved answer pllzz

Varun.Rawat · Accepted Answer

Hi Christina,
Please find below the solution to the asked query :
The given quadratic equation is,3x2+7x +p = 0Since, x = -2 is a root of the above equation, so it must satisfy it
Put x = -2 in the above equation, we get3-22+7-2+p = 0⇒12-14+p = 0⇒p=2Now, the given quadratic equation is,    x2 + k4x+k-1 + p = 0⇒x2 + 4kx + k2-k+2 = 0Now, a = 1; b = 4k; c = k2-k+2Now, D = b2 - 4ac = 4k2 - 41k2-k+2 = 16k2-4k2+4k-8 So, D = 12k2+4k-8Now, the above equation has equal roots, then     D = 0⇒12k2+4k-8 = 0⇒3k2 + k - 2 = 0⇒3k2 + 3k - 2k - 2 = 0⇒3kk+1 - 2k+1 = 0⇒3k-2k+1 = 0⇒3k-2 = 0  or  k+1 =0⇒k = 23   or  k = -1

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if x is = -2 is a root of the equation 3x2 +7x +p =0 . find the values of k so that the roots of the equation x2 +k (4x+k-1)+p=0 are equal .solved answer pllzz..

if x is = -2 is a root of the equation 3x²+7x +p =0 . find the values of k so that the roots of the equation x² +k (4x+k-1)+p=0 are equal .
solved answer pllzz..