Question

Find the roots of the following quadratis
lequations , if they exist.
5x^2-7x-6=0​

Answer 1

Correct Question

• Find the roots of the following quadratic equation 5x² - 7x - 6 = 0.

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Given Equation

• 5x² - 7x - 6 = 0

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To find

• Roots of the quadratic equation.

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Solution

• We will solve this question by quadratic formula.
• To apply the formula, we need to calculate the discriminant (D).

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{D = b^2 - 4ac{\bigstar}}}}$

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Here,

• a = 5
• b = -7
• c = -6

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$\large{\tt{\longmapsto{D = (-7)^2 - 4(5)(-6)}}}$

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$\large{\tt{\longmapsto{D = 49 + 120}}}$

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$\large{\tt{\longmapsto{D = 169}}}$

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★ Using Quadratic Formula

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{x = \dfrac{-b ± \sqrt{D}}{2a}{\bigstar}}}}$

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Here,

• b = -7
• D = 169
• a = 5

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★ Putting values in the formula

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{-(-7) ± \sqrt{169}}{2(5)}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{7 ± 13}{10}}$

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Root 1

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{7 - 13}{10}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{-6}{10}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{-3}{5}}$

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Root 2

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{7 + 13}{10}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{20}{10}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = 2}$

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Hence, the roots are :-

$\tt\longrightarrow{}$ $\bf{x = \dfrac{-3}{5}\: or\: x = 2}$

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