TS EAMCET · Maths · Quadratic Equation
If the quotient and remainder obtained when the expression \(3 x^5-6 x^4+2 x^3+4 x^2-5 x+8\) is divided by the expression \(x^2-2 x+3\) are \(a x^3+b x^2+c x+d\) and \(p x+q\) respectively, then \(a b+c d=\)
- A \(p+2 q\)
- B \(p+2 q-2\)
- C \(\approx 2 p+q\)
- D \(2 p+q-2\)
Answer & Solution
Correct Answer
(B) \(p+2 q-2\)
Step-by-step Solution
Detailed explanation
\( (3x^5-6x^4+2x^3+4x^2-5x+8) \div (x^2-2x+3) = (3x^3-7x-10) \text{ with remainder } (-4x+38) \) \( a=3, b=0, c=-7, d=-10 \) \( p=-4, q=38 \) \( ab+cd = (3)(0) + (-7)(-10) = 0 + 70 = 70 \) \( p+2q-2 = (-4) + 2(38) - 2 = -4 + 76 - 2 = 70 \) So, \( ab+cd\) = \( p+2q-2\)
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