The sum of all real value of x for which 3x2-9x-17x2-3x-10-5x2-7x-193x2-5x-12 is equal to

3x^2 9x+17x^2+3x+10=5x^2 7x+193x^2+5x+12 ⇒ 3x^2 9x+175x^2 7x+19=x^2+3x+103x^2+5x+12 ⇒ 3x^2 9x+175x^2 7x+19 1=x^2+3x+103x^2+5x+12 1 ⇒ 2x^2 2x 25x^2 7x+19= 2x^2 ...

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Byju's Answer

Standard XII

Mathematics

Determinant

The sum of al...

Question

The sum of all real value of $x$ for which $\frac{3 x^{2} - 9 x + 17}{x^{2} + 3 x + 10} = \frac{5 x^{2} - 7 x + 19}{3 x^{2} + 5 x + 12}$ is equal to

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Solution

$\frac{3 x^{2} - 9 x + 17}{x^{2} + 3 x + 10} = \frac{5 x^{2} - 7 x + 19}{3 x^{2} + 5 x + 12}$

$\Rightarrow \frac{3 x^{2} - 9 x + 17}{5 x^{2} - 7 x + 19} = \frac{x^{2} + 3 x + 10}{3 x^{2} + 5 x + 12}$
$\Rightarrow \frac{3 x^{2} - 9 x + 17}{5 x^{2} - 7 x + 19} - 1 = \frac{x^{2} + 3 x + 10}{3 x^{2} + 5 x + 12} - 1$
$\Rightarrow \frac{- 2 x^{2} - 2 x - 2}{5 x^{2} - 7 x + 19} = \frac{- 2 x^{2} - 2 x - 2}{3 x^{2} + 5 x + 12}$

or
$\Rightarrow \begin{matrix} E i t h e r x^{2} + x + 1 = 0 & 5 x^{2} - 7 x + 19 No real roots & = 3 x^{2} + 5 x + 12 2 x^{2} - 12 x + 7 = 0 sum of roots = 6 \end{matrix}$

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The sum of all real value of x for which 3x2−9x+17x2+3x+10=5x2−7x+193x2+5x+12 is equal to

3x2−9x+17x2+3x+10=5x2−7x+193x2+5x+12 ⇒ 3x2−9x+175x2−7x+19=x2+3x+103x2+5x+12 ⇒ 3x2−9x+175x2−7x+19−1=x2+3x+103x2+5x+12−1 ⇒ −2x2−2x−25x2−7x+19=−2x2−2x−23x2+5x+12 or ⇒Either x2+x+1=05x2−7x+19No real roots =3x2+5x+122x2−12x+7=0sum of roots = 6

The sum of all real value of $x$ for which $\frac{3 x^{2} - 9 x + 17}{x^{2} + 3 x + 10} = \frac{5 x^{2} - 7 x + 19}{3 x^{2} + 5 x + 12}$ is equal to