Which of the following equations has $2$ as one of the roots?

x^{2} + 4 x - 5 = 0

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x^{2} + 3 x + 12 = 0

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2 x^{2} - 7 x + 6 = 0

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3 x^{2} - 6 x + 2 = 0

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Solution

The correct option is C $2 x^{2} - 7 x + 6 = 0$
Substituting $x = 2$ in given equations
$A :$
$x^{2} + 4 x - 5 \Rightarrow (2^{2}) + 4 \times 2 - 5 \Rightarrow 4 + 8 - 5 = 7$

$B :$
$x^{2} + 3 x + 12 \Rightarrow (2^{2}) + 3 \times 2 + 12 \Rightarrow 4 + 6 + 12 = 22$

$C :$
$2 x^{2} - 7 x + 6 \Rightarrow 2 (2^{2}) - 7 \times 2 + 6 \Rightarrow 8 - 14 + 6 = 0$

$D :$
$3 x^{2} - 6 x + 2 \Rightarrow 3 (2^{2}) - 6 \times 2 + 2 \Rightarrow 12 - 12 + 2 = 2$

Then $(C)$ equation has $2$ as a root.

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Similar questions

Question 3
Which of the following equations has 2 as a root?
(a) $x^{2} - 4 x + 5 = 0$
(b) $x^{2} + 3 x - 12 = 0$
(c) $2 x^{2} - 7 x + 6 = 0$
(d) $3 x^{2} - 6 x - 2 = 0$

Question 3
Which of the following equations has 2 as a root?
(a) $x^{2} - 4 x + 5 = 0$
(b) $x^{2} + 3 x - 12 = 0$
(c) $2 x^{2} - 7 x + 6 = 0$
(d) $3 x^{2} - 6 x - 2 = 0$

Question 10
Which of the following equations has no real roots?
(A) $x^{2} - 4 x + 3 \sqrt{2} = 0$
(B) $x^{2} + 4 x - 3 \sqrt{2} = 0$
(C) $x^{2} - 4 x - 3 \sqrt{2} = 0$
(D) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$

Q. Find the nature of the roots of the following quadratic equation:

3 x^{2} + 7 x + 2 = 0

{(x + 3)}^{2} + 4 x + 7 = 0

2 x^{2} - 8 x + 34 = 0

x^{2} + 2 \sqrt{3 x} - 1 = 0

Q. If p, q are the roots of the equation

x^{2} - 3 x + 2 = 0

, find the equation which has roots as (2p + 1) and (2q + 1).

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Which of the following equations has 2 as one of the roots?

The correct option is C 2x2−7x+6=0Substituting x=2 in given equations A:x2+4x−5⇒(22)+4×2−5⇒4+8−5=7B:x2+3x+12⇒(22)+3×2+12⇒4+6+12=22C:2x2−7x+6⇒2(22)−7×2+6⇒8−14+6=0D:3x2−6x+2⇒3(22)−6×2+2⇒12−12+2=2Then (C) equation has 2 as a root.

Which of the following equations has $2$ as one of the roots?