1.

If the HCF of x²+x-12 and 2x² -kx-9 is x-k , find the value of 'k'.

Answer»

HCF of x²+x-12 and 2x² -kx-9 is x-k so (x-k) is a FACTOR of both the polynomials. So x=k is a zero of both the polynomials. So F(k)=0 in both cases. thus

k² + k - 12 = 0    --------------(1)
2k² - k² - 9 = 0    --------------(2)

from EQUATION 1, k = 3,-4
from equation 2, k = +3, -3
+3 is common to both the SOLUTIONS. 
So value of k is 3.


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