The sum of the roots of the equation,{x^2} + | vedclass

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(C) Given equation: ${x^2} + |2x - 3| - 4 = 0$Case $I$: If $x \ge \frac{3}{2}$,then $|2x - 3| = 2x - 3$.The equation becomes: ${x^2} + 2x - 3 - 4 = 0

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$\sqrt{2}$

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(C) Given equation: ${x^2} + |2x - 3| - 4 = 0$Case $I$: If $x \ge \frac{3}{2}$,then $|2x - 3| = 2x - 3$.The equation becomes: ${x^2} + 2x - 3 - 4 = 0 \Rightarrow {x^2} + 2x - 7 = 0$.Roots are $x = \frac{-2 \pm \sqrt{4 - 4(1)(-7)}}{2} = \frac{-2 \pm \sqrt{32}}{2} = -1 \pm 2\sqrt{2}$.Since $x \ge \frac{3}{2}$,we check the values: $-1 + 2\sqrt{2} \approx -1 + 2.828 = 1.828 > 1.5$ (Valid).$-1 - 2\sqrt{2} \approx -3.828 So,$x_1 = 2\sqrt{2} - 1$.Case $II$: If $x The equation becomes: ${x^2} - 2x + 3 - 4 = 0 \Rightarrow {x^2} - 2x - 1 = 0$.Roots are $x = \frac{2 \pm \sqrt{4 - 4(1)(-1)}}{2} = \frac{2 \pm \sqrt{8}}{2} = 1 \pm \sqrt{2}$.Since $x  1.5$ (Invalid).$1 - \sqrt{2} \approx -0.414 So,$x_2 = 1 - \sqrt{2}$.The sum of the valid roots is $(2\sqrt{2} - 1) + (1 - \sqrt{2}) = \sqrt{2}$.

The sum of the roots of the equation,${x^2} + |2x - 3| - 4 = 0$,is

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Solve the given two equations and select the correct answer from the given options:
$I. 6x^{2} + 29x + 35 = 0$
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The sum of the roots of the equation,${x^2} + |2x - 3| - 4 = 0$,is

Similar Questions

Solve the given two equations and select the correct answer from the given options:$I. 6x^{2} + 29x + 35 = 0$$II. 3y^{2} + 19y + 30 = 0$

Solve the given two equations and select the correct option.

Solve the given two equations and select the correct option.

If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$,then:

Solve the given two equations and select the correct answer from the given options.$I.$ $x^{3} \times 13 = x^{2} \times 247$$II.$ $y^{1 / 3} \times 14 = 294 \div y^{2 / 3}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Solve the given two equations and select the correct answer from the given options:
$I. 6x^{2} + 29x + 35 = 0$
$II. 3y^{2} + 19y + 30 = 0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{3} \times 13 = x^{2} \times 247$
$II.$ $y^{1 / 3} \times 14 = 294 \div y^{2 / 3}$