Question

If x = – 4 is a root of the equation x2 + 2x + 4p = 0, find the values of k for which the equation x2 + px (1 + 3k) + 7 (3 + 2k) = 0 has equal roots

Answer 1

(-4)² +2(-4) + 4p = 0

16 -8 = -4p

8 = -4p

p = -2

x² + px (1 + 3k) + 7 (3 + 2k) = 0

For equal roots

D = 0

0 = b²-4ac

0 = 4(1+3k)² - 28(3+2k)

0 = 4+36k² + 24k -84 - 56k

0 = 36k² -32 k -80

0 = 9k² - 8k - 20

0 = 9k² -18 k +10k -20

0 = 9k(k-2) + 10(k-2)

0 = (k-2)(9k+10)

K= 2 , -9/10

k = 2

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