Question

solve quadratic equation by completeing square method. 2x^2+13x+15=0

Answer 1

I think this is the answer

Answer 2

Answer:

The roots of the quadratic equation are

$∴ \: x = - 5 \: \: or \: \: x = \frac{ - 3}{2}$

Step-by-step-explanation:

NOTE: Kindly see the attachment first.

The given quadratic equation is

2x² + 13x + 15 = 0

$∴ \: {x}^{2} + \frac{13}{2} x + \frac{15}{2} = 0 \: \: ...( \: dividing \: by \: 2 \: ) \\ \\ comparing \: {x}^{2} + \frac{13}{2} x \: with \: {x}^{2} + 2xy \\ \\ ∴ \: 2xy = \frac{13}{2} x \\ \\ ∴ \: y = \frac{13}{4} \\ \\ ∴ \: {y}^{2} = {( \frac{13}{4} )}^{2} = \frac{ {13}^{2} }{ {4}^{2} } = \frac{169}{16} \\ \\ ∴ \: {y}^{2} = \frac{169}{16} \\ \\ ∴ \: {x}^{2} + \frac{13}{2} x + \frac{169}{16} - \frac{169}{16} + \frac{15}{2} = 0 \\ \\ ∴ \: {(x + \frac{13}{4} )}^{2} - ( \frac{169 - 120}{16} = 0 \\ \\ ∴ \: {(x + \frac{13}{4}) }^{2} - ( \frac{49}{16} ) = 0 \\ \\ ∴ \: {(x + \frac{13}{4} )}^{2} - {( \frac{7}{4} )}^{2} = 0 \\ \\ ∴ \: (x + \frac{13}{4} + \frac{7}{4} ) \: (x + \frac{13}{4} - \frac{7}{4} ) \: \: ...( \: {a}^{2} - {b}^{2} = ( \: a + b \: ) \: ( \: a - b \: ) \: ) \\ \\ ∴ \: (x + \frac{20}{4} ) \: (x + \frac{6}{4} ) = 0 \\ \\ ∴ \: (x + 5) \: (x + \frac{3}{2} ) = 0 \\ \\ ∴ \: (x + 5) = 0 \: \: or \: \: (x + \frac{3}{2} ) = 0 \\ \\ ∴ \: x + 5 = 0 \: \: or \: \: x + \frac{3}{2} = 0 \\ \\ ∴ \: x = - 5 \: \: \: or \: \: \: x = \frac{ - 3}{2}$

Ans.: The roots of the quadratic equation are

$∴ \: x = - 5 \: \: or \: \: x = \frac{ - 3}{2}$

Additional Information:

1. Quadratic Equation :

An equation having a degree '2' is called quadratic equation.

The general form of quadratic equation is

ax² + bx + c = 0

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Completing Square Method:

To solve a quadratic equation by completing square method, we have to follow some steps. Those are as :-

1) Write the given equation in the form ax² + bx + c = 0.

2) Consider the first two terms on LHS, and find the third suitable square term to make the polynomial a perfect square.

3) Add the square term formed and subtract that term to the given equation.

4) Write the square of the first three terms and the last two terms.

5) Factorize the term and make equal it to zero.

6) Find the value of the variable.