Question

Solve the following questions.

1) If 2 is a root of the quadratic equation 3x" + px - 8 = 0 and the quadratic equation 4x” – 2px + k = 0 has real and equal roots, find k. 2​

Answer 1

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⇒  3x2+px−8=0

Substitute x=2, since 2 is root of equation

⇒  3(2)2+p(2)−8=0

⇒  12+2p−8=0

⇒  4+2p=0

∴  p=−2

⇒  4x2−2px+k=0

⇒  4x2−2(−2)x+k=0           [ Since, p=−2 ]

⇒  4x2+4x+k=0

⇒  Here, a=4,b=4,c=k

⇒  It is given that roots are equal.

∴  b2−4ac=0

⇒  (4)2−4(4)(k)=0

⇒  16−16k=0

=>16k=16

∴k=1