The roots of the equation 2x2 – 5x - 3 = 0 are k less than those of the equation ax2 + bx + c = 0. Which of the following could be true?
Explanation:
The roots of the equation 2x2 – 5x - 3 = 0 are 3 and -1/2.
Now the roots of the equation ax2 + bx + c = 0 are k more than these roots.
Hence, roots of ax2 + bx + c = 0 are 3 + k and -1/2 + k.
⇒ x = 3 + k should satisfy the given equation.
⇒ a(3 + k)2 + b(3 + k) + c = 0
⇒ ak2 + 6ak + 9a + 3b + kb + c = 0
⇒ ak2 + 6ak + kb + 9a + 3b + c = 0
⇒ k(ak + 6a + b) + 9a + 3b + c = 0
Hence, option (c).
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