Question

Solve the following two quadratic equations by factorisation method..
1} m²-14m+13=0
2} 3x²-x-10=0
Answer should be respective and correct otherwise I will report!!!!!!​

Answer 1

EXPLANATION.

Solve quadratic equation by factorization method.

METHOD = 1.

(1) = m² - 14m + 13 = 0.

factorizes into middle term split.

⇒ m² - 13m - m + 13 = 0.

⇒ m ( m - 13 ) - 1 ( m - 13 ) = 0.

⇒ ( m - 1 ) ( m - 13 ) = 0.

⇒ m = 1  and  m = 13.

(2) = 3x² - x - 10 = 0.

Factorizes into middle term split,

⇒ 3x² - 6x + 5x - 10 = 0.

⇒ 3x ( x - 2 ) + 5 ( x - 2 ) = 0.

⇒ ( 3x + 5 ) ( x - 2 ) = 0.

⇒ x = -5/3  and  x = 2.

METHOD = 2.

(1) = m² - 14m + 13 = 0.

To find Discriminant = D,

⇒ D = b² - 4ac

⇒ D = (-14)² - 4(1)(13).

⇒ D = 196 - 52.

⇒ D = 144.

Formula for x = -b ± √D/2a.

⇒ - (-14) ± √144/2.

⇒ 14 ± 12/2.

⇒ 14 + 12/2  and  14 - 12/2.

⇒ 13  and  1.

Value of x = 13  and  1.

(2) = 3x² - x - 10 =0.

To find the discriminant. D = 0.

⇒ D = (-1)² - 4(3)(-10).

⇒ D = 1 + 120.

⇒ D = 121.

To find x = -b ± √D/2a.

⇒ - (-1) ± √121/2(3).

⇒ 1 ± 11/6.

⇒ 1 + 11/6  and  1 - 11/6.

⇒ 2  and -5/3

Value of x = 2  and  -5/3.

Answer 2

✯SoluTion:

Given,

Quadratic Equation

☞ m²-14m+13 = 0

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ $\purple{\sf{13m² = -13m × -1m}}$

$→\;{\bf{m²-13m-m+13 = 0}}$

$→\;{\bf{m(m-13)-1(m-13) = 0}}$

$→\;{\bf{(m-13)(m-1) = 0}}$

The Roots of the Equation are

◕➜ $\Large\fbox\red{\sf{m = 13\;or\;1}}$

_________________________

Given,

Quadratic Equations

☞ 3x²-x-10 = 0

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ $\purple{\sf{30x² = -6x × 5x}}$

$→\;{\bf{3x²-6x+5x-10 = 0}}$

$→\;{\bf{3x(x-2)+5(x-2) = 0}}$

$→\!{\bf{(3x-5)(x-2) = 0}}$

The Roots of the Equation are

◕➜ $\Large\boxed{\red{\sf{x = \frac{-5}{3}\;or\;2}}}$

Hope It Helps You ✌️