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MODEL PAPER 8 (STANDARD) — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMODEL PAPER 8 (STANDARD)1 Mark
MCQ
Let $b=a+c$. Then the equation $ax ^2+ bx + c =0$ has equal roots if
  • A
    $a = -c$
  • ✓
    $a = c$
  • C
    $a = -2c$
  • D
    $a = 2c$
✓

Answer

Correct option: B.
$a = c$
Since, If $a x^2+b x+c=0$ has equal roots, then
$b^2-4 ac=0$
$\Rightarrow(a+c)^2-4 ac=0 \ldots[\text { Given: } b=a+c]$
$\Rightarrow a^2+c^2+2 ac-4 ac=0$
$\Rightarrow a^2+c^2-2 ac=0$
$\Rightarrow(a-c)^2=0$
$\Rightarrow a-c=0$
$\Rightarrow a=c$

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