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Quadratic Equations in One Variable — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsQuadratic Equations in One Variable1 Mark
MCQ
Which of the following equations has two distinct real roots?
  • A
    $2 x^2-3 \sqrt{2} x+\frac{9}{4}=0$
  • B
    $x^2+x-5=0$
  • C
    $x^2+3 x+2 \sqrt{2}=0$
  • D
    $5 x^2-3 x+1=0$
✓

Answer

$
\begin{aligned}
& 2 x^2-3 \sqrt{2} x+\frac{9}{4}=0 \\
& b^2-4 a c \\
& =(-3 \sqrt{2})^2-4 \times 2 \times \frac{9}{4} \\
& =18-18 \\
& =0 \\
& \therefore \text { Roots are real and equal. } \\
& x^2+x-5=0 \\
& b^2-4 a c \\
& =(1)^2-4 \times 1 \times(-5) \\
& =1+20 \\
& =\sqrt{21}>0
\end{aligned}
$
$\therefore$ Roots are real and distinct.

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