MCQ
Which of the following equations has two distinct real roots?
- A$2 x^2-3 \sqrt{2} x+\frac{9}{4}=0$
- ✓$x^2+x-5=0$
- C$x^2+3 x+2 \sqrt{2}=0$
- D$5 x^2-3 x+1=0$
✓
Answer
Correct option: B.
$x^2+x-5=0$
(b) : To have two distinct real roots, discriminant $\left(D=b^2-4 a c\right)$ must be $>0$.
(a) $D=(-3 \sqrt{2})^2-4(2) \times\left(\frac{9}{4}\right)=18-18=0$
(b) $D=(1)^2-4(1)(-5)=1+20=21>0$
(c) $D=(3)^2-4(1)(2 \sqrt{2})=9-8 \sqrt{2}<0$
(d) $D=(-3)^2-4(5)(1)=9-20=-11<0$
(a) $D=(-3 \sqrt{2})^2-4(2) \times\left(\frac{9}{4}\right)=18-18=0$
(b) $D=(1)^2-4(1)(-5)=1+20=21>0$
(c) $D=(3)^2-4(1)(2 \sqrt{2})=9-8 \sqrt{2}<0$
(d) $D=(-3)^2-4(5)(1)=9-20=-11<0$
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