Find the value of k for which x=3 is a solution of the quadratic equation, (k+2)x2−kx+6=0. Thus find the other root of the equation.
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Solution
Given : (k+2)x2−kx+6=0 Putting x=3 (k+2)×9−k×3+6=0 9k+18−3k+6=0 6k=−24 k=−4 Putting k=−4 in given equation −2x2+4x+6=0 x2−2x−3=0 x2−3x+x−3=0 x(x−3)+1(x−3)=0 (x+1)(x−3)=0 x+1=0 or x−3=0 x=−1 or x=3 Other root of the equation, x=−1