TS EAMCET · Maths · Quadratic Equation
The equation having the multiple root of the equation \(x^4+4 x^3-16 x-16=0\) as its root is
- A \(x^2+2 x-3=0\)
- B \(x^2-3 x+2=0\)
- C \(x^2+x-2=0\)
- D \(x^2-4 x+3=0\)
Answer & Solution
Correct Answer
(C) \(x^2+x-2=0\)
Step-by-step Solution
Detailed explanation
\(f(x) = x^4+4 x^3-16 x-16\) \(f'(x) = 4x^3+12x^2-16\) \(f'(x)=0 \implies x^3+3x^2-4=0\) \((x-1)(x+2)^2=0 \implies x=1, x=-2\) \(f(1) = 1+4-16-16 = -27 \neq 0\) \(f(-2) = (-2)^4+4(-2)^3-16(-2)-16 = 16-32+32-16 = 0\) The multiple root is \(x=-2\). Check option C: \(x^2+x-2=0\)…
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