Question

Find the value of kwhich one rooy of quadratic equation kx2-14x+8=0is 2 .Find the value of kfor which the equation x2+5kx+16=0has real and equal roots

Answer 1

¥first part .
given that 2 is a root of equation,
so put 2 in place of x
kx²-14x+8=0
k(2)²-14(2)+8=0
4k-28+8=0
4k-20=0
4k=20
k=20/4
k=5

¥second part.
x²+5kx+16=0
for real and equal roots, discriminant (D)=0
where D=b²-4ac
in equation, a=1, b=5k and c=16
by filling values
(5k)²-4(1)(16)
25k²-64=0
25k²=64
k²=64/25
k=√64/25
k=√64/5

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