1.

In the polynomial x2 + kx + 6, what number must be taken ask to get a polynomial for which x –1 is a factor? Find also the other factor of that polynomial.

Answer»

p (x) = x2 + kx + 6

If (x – 1) is a factor of p(x)

then p(1) = 0

p(1) = 12 + k x 1 + 6 = 7 + k

7 + k = 0

k= –7

\(\therefore\) p(x) = x2 – 7x + 6

a + b = 7

ab = 6

a= 1, b = 6

factors are (x – 1 )(x – 6)

Second factor is (x – 6)



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