If the equation ax^4 + x^3 - x^2 + 3x + 2 = 0 and ax^4 - x^2 + 3x + 1 = 0 have a common root, then find the value of a.
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Answer:
6
Solution
x2−3x+b=0 ……(1)
Let the roots are α+β.
x3−4x2+qx+0……(2)
One root of the equation is zero and other root is repeated
then roots are 0,β,β, then
Sum of roots 2β=4
∴β=2
α+β=3 by equation (1)
∴α=1
∴b=αβ=2
q=0β+β2+β0=β2=4
∴(b+q)=(2+4)=6
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