AP EAMCET · Maths · Quadratic Equation
If \(x^2-5 x+6\) is a factor of \(f(x)=x^4-17 x^3+k x^2-247 x+210\), then the other quadratic factor of \(f(x)\) is
- A \(x^2+12 x+35\)
- B \(x^2-12 x+35\)
- C \(x^2-6 x+35\)
- D \(x^2+6 x+35\)
Answer & Solution
Correct Answer
(B) \(x^2-12 x+35\)
Step-by-step Solution
Detailed explanation
\( (x^2-5x+6)(x^2+bx+c) = x^4-17 x^3+k x^2-247 x+210 \) \( x^4 + (b-5)x^3 + (c-5b+6)x^2 + (-5c+6b)x + 6c = x^4-17 x^3+k x^2-247 x+210 \) \( b-5 = -17 \implies b = -12 \) \( 6c = 210 \implies c = 35 \) \( \text{The other quadratic factor is } x^2-12x+35 \)
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