Which of the following equation has $(- 1)$ as a root ?

x^{2} + 3 x - 10 = 0

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x^{2} - x - 12 = 0

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3 x^{2} - 2 x - 5 = 0

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9 x^{2} + 24 x + 16 = 0

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Solution

The correct option is B $3 x^{2} - 2 x - 5 = 0$
$3 x^{2} - 2 x - 5 = 0$
$\Rightarrow 3 x^{2} - 5 x + 3 x - 5 = 0$
$\Rightarrow x (3 x - 5) + 1 (3 x - 5) = 0$
$\Rightarrow (x + 1) (3 x - 5) = 0$
$\Rightarrow x = - 1 o r x = 5 / 3$
$∴$ Option (c) has -1 as a root

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Similar questions

Q. Which of the following equations has the sum of its roots as 3?

(a) x² + 3x − 5 = 0

(b) −x² + 3x + 3 = 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. Question 5
Which of the following equations has the sum of its roots as 3?
(a)

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

(b)

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

(c)

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

(d)

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

Question 5
Which of the following equations has the sum of its roots as 3?
(a) $2 x^{2} - 3 x + 6 = 0$
(b) $- x^{2} + 3 x - 3 = 0$
(c) $\sqrt{2} x^{2} - \frac{3}{\sqrt{2}} x + 1 = 0$
(d) $3 x^{2} - 3 x + 3 = 0$

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

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Which of the following equation has (−1) as a root ?

The correct option is B 3x2−2x−5=03x2−2x−5=0⇒3x2−5x+3x−5=0⇒x(3x−5)+1(3x−5)=0⇒(x+1)(3x−5)=0⇒x=−1orx=5/3∴ Option (c) has -1 as a root

Which of the following equation has $(- 1)$ as a root ?

The correct option is B $3 x^{2} - 2 x - 5 = 0$
$3 x^{2} - 2 x - 5 = 0$
$\Rightarrow 3 x^{2} - 5 x + 3 x - 5 = 0$
$\Rightarrow x (3 x - 5) + 1 (3 x - 5) = 0$
$\Rightarrow (x + 1) (3 x - 5) = 0$
$\Rightarrow x = - 1 o r x = 5 / 3$
$∴$ Option (c) has -1 as a root