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Quadratic Equations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSQuadratic Equations1 Mark
MCQ
If $\alpha,\beta$ are the roots of the equation $x^2− p(x + 1) − c = 0$, then $(\alpha+1)(\beta+1)=$
  • A
    c
  • B
    c - 1
  • ✓
    1 - c
  • D
    None of these.
✓

Answer

Correct option: C.
1 - c
  1. 1 - c
Solution:
Given equation:
$x^2 − p(x + 1) − c = 0$
or $x^2 − px − p − c = 0$
Also $\alpha $ and $\beta$ are the roots of the equation.
Sum of the roots $=\alpha+\beta=\text{p}$
Product of the roots $=\alpha\beta=-(\text{c}+\text{p})$
Then, $(\alpha+1)(\beta+1)=\alpha\beta+\alpha+\beta+1$
$=-(\text{c}+\text{p})+\text{p}+1$
$=1-\text{c}$
$=-\text{c}-\text{p}+\text{p}+1$

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