Question

Find the value(s) of k if the quadratic equation
x^2 − (k + 2)x + k + 1 = 0 has:
a. equal roots
b. one root equal to 5
c. consecutive roots
d. one root double the other
e. reciprocal roots

Answer 1

Answer:

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Answer 2

Given, x

2

+k(2x+k−1)+2=0

Simplify above equation:

x

2

+2kx+(k

2

−k+2)=0

Compare given equation with the general form of quadratic equation, which ax

2

+bx+c=0

here, a=1,b=2k,c=(k

2

−k+2)

Find discriminant:

D=b

2

−4ac

=(2k)

2

−4×1×(k

2

−k+2)

=4k

2

−4k

2

+4k−8

=4k−8

Since roots are real and equal (given)

Put D=0

4k−8=0

k=2

Hence, the value of k is 2.