Question:
Find the value of k so that g(x)=x^2 +2x-3 is a factor of p(x)=2x^4 +x^3-14x^2-kx+ 6 Hence find all the zeroes of p(x)
Answer:
Given, g(x) = x2 + 2x - 3 is a factor of p(x) = 2x4 + x3 - 14x2 - kx + 6
Since g(x) is a factor of p(x), So the remainder should be zero after p(x)/g(x)
Hence, -(k + 5) = 0
=> k + 5 = 0
=> k = -5
So, the value of k is -5
Now, the polynomial is
2x4 + x3 - 14x2 + 5x + 6 = (x2 + 2x - 3)*(2x2 - 3x - 2)
= (x + 3)*(x - 1)*(x - 2)*(2x + 1)
So, the zeroes of polynomials are: -3, 1, 2, -1/2
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