Question

find the number of real root of 3^2x^2-7x+7 =9

Answer 1

Concept Introduction: Quadratic equations are very special equations.

Given:

We have been Given:

${3}^{2 {x}^{2} - 7x + 7} = 9$

To Find:

We have to Find: find the number of real root

Solution:

According to the problem, Simplifying the equation we get,

${3}^{2 {x}^{2} - 7x + 7} = {3}^{2}$

therefore,

$2 {x}^{2} - 7x + 7 = 2 \\ 2 {x}^{2} - 7x + 5 = 0$

therefore applying the roots Equation, therefore the values are,

$a = 2 \\ b = - 7 \\ c = 5$

therefore,

$d = \sqrt{ {b}^{2} - 4ac} \\ d = \sqrt{ {( - 7)}^{2} - 4 \times 2 \times 5} \\ d = \sqrt{49 - 40} \\ d = \sqrt{9} \\ d = 3 > 0$

therefore, the equation has TWO roots.

Final Answer: The Equation has TWO roots.

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