Which of the following equations has the sum of it's roots as 3 ?
(a) 2x² - 3x + 6 = 0
(b) -x² + 3x-3 = 0
(c) rt2x² - 2/rt2 x +1 = 0
(d) 3x² - 3x + 3 = 0

Question

Which of the following equations has the sum of it's roots as 3
?
(a) 2x2 - 3x + 6 = 0
(b) -x2 + 3x-3 = 0
(c) rt2x2 - 2/rt2 x +1 = 0
(d) 3x2 - 3x + 3 = 0

Vimala · Accepted Answer

Consider the general quadratic equation

$a x^{2} + b x + c = 0$

Sum of the roots of the equation $a x^{2} + b x + c = 0$ is given by $\frac{- b}{a}$ .

Thus, the sum of the roots of the equation $2 x^{2} - 3 x + 6 = 0$ is given by $- \frac{(- 3)}{2} = \frac{3}{2}$

The sum of the roots of the equation $- x^{2} + 3 x - 3 = 0$ is given by $- \frac{3}{- 1} = 3$

The sum of the roots of the equation $\sqrt{2} x^{2} - \frac{2}{\sqrt{2}} x + 1 = 0$ is given by $- \frac{\frac{- 2}{\sqrt{2}}}{\sqrt{2}} = 1$

The sum of the roots of the equation $3 x^{2} - 3 x + 3 = 0$ is given by $- \frac{- 3}{3} = 1$

Therefore, only in option (b), that is for the equation $- x^{2} + 3 x - 3 = 0$ , the sum of the roots is given by 3.

Hence option (b) is the correct answer.

Which of the following equations has the sum of it's roots as 3 ?(a) 2x2 - 3x + 6 = 0(b) -x2 + 3x-3 = 0(c) rt2x2 - 2/rt2 x +1 = 0(d) 3x2 - 3x + 3 = 0

Which of the following equations has the sum of it's roots as 3 ?
(a) 2x² - 3x + 6 = 0
(b) -x² + 3x-3 = 0
(c) rt2x² - 2/rt2 x +1 = 0
(d) 3x² - 3x + 3 = 0