Question

x
$m {2 - 14m + 13 = 0}^{?}$
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Answer 1

$\sf{Answer}$

Given Quadratic equation to solve m² - 14m + 13 = 0

So,

m² - 14m + 13 = 0

Finding factors :-

Here the sum of factors should be - 14m & product of factors should be 13m²

1 m × 13m = 13m²

13m × 1m = 13m²

- 1 m × - 13m = 13m²

- 13m × -1m = 13m²

If you observe the factors

Here the sum should be - 14m Product should be 13m²

- 13m × - 1m = 13m²

-13m - m = -14m

Condition satisfied

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So, split the middle term as - 13m - m

Splitting the middle term

m² - 14m + 13 = 0

m² - 13m - m + 13 = 0

Taking common

m ( m - 13 ) -1 ( m -13) = 0

Again take common

(m - 13) ( m- 1) = 0

Equate both to zero

Case 1 :-

m - 13 = 0

m = 13

Case - 2:-

m - 1 = 0

m = 1

So, the values of m are 13, 1

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Know more :-

General form of Quadratic equation is

ax² + bx + c = 0

• A quadratic equation has 2 roots
• We can find those two roots by different methods like
• FACTORISATION METHOD
• QUADRATIC FORMULA
• COMPLETE SQUARING etc

Nature of roots :-

It can be determined by discriminant of Quadratic equation

Nature of roots :- Whether the roots are complex , equal , real

It can be determined by discriminant

D = b² - 4ac

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