ICSE Class X Math 2015 Solved Paper

Question : 15

Total: 52

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.

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
(−4+2)x2−(−4)x+6‌=0
−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

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