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Polynomials — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPolynomials1 Mark
MCQ
Choose the correct answer from the given four options in the following questions:If the zeroes of the quadratic polynomial $x^2+(a+1) x+b$ are 2 and -3, then:
  • A
    a = -7, b = -1.
  • B
    a = 5, b = -1.
  • C
    a = 2, b = -1.
  • ✓
    a = 0, b = -6.
✓

Answer

Correct option: D.
a = 0, b = -6.
Let $p(x) = x^2 + (a + 1)x + b$Given that, 2 and -3 are the zeroes of the quadratic polynomial p(x).
$\therefore p(2)=0 \text { and } p(-3)=0$
$\Rightarrow 2^2+(a+1)(2)+b=0$
$\Rightarrow 4+2 a+2+b=0$
$\Rightarrow 2 a+b=-6 \ldots . .(i)$
$\text { and }(-3)^2+(a+1)(-3)+b=0$
$\Rightarrow 9-3 a-3+b=0$
$\Rightarrow 3 a-b=6 \ldots . . .(i i)$
On adding Eqs. (i) and (ii), we get
$5 a=0 \Rightarrow a=0$
Put the value of a in Eq. (i), we get
$2 \times 0+b=-6 \Rightarrow b=-6$
required values are $a=0$ and $b=-6$.

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