Question

The root of quadratic equation xsquare -5x-6=0

Answer 1

EXPLANATION.

Quadratic equation.

⇒ x² - 5x - 6 = 0.

As we know that,

Factorizes into middle term splits, we get.

⇒ x² - 6x + x - 6 = 0.

⇒ x(x - 6) + 1(x - 6) = 0.

⇒ (x + 1)(x - 6) = 0.

⇒ x = -1  and  x = 6.

                                                                                                                             

MORE INFORMATION.

Nature of the factors of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.

Answer 2

Required answer -

Question -

• The root of a quadratic equation is x²-5x-6=0

Given that -

• The root of a quadratic equation is x²-5x-6=0

To determine -

• Value of x.

Using concept -

• Middle term splitting method.

Full solution -

→ x²-5x-6=0

→ x²-6x+x-6 = 0

→ x(x-6) + 1(x-6) = 0

→ (x+1)(x-6) = 0

→ x = -1 or x = 6

• Henceforth, x = -1 or +6

Additional information -

Question 1) What is factorisation?

Answer - Let's see what is factorisation by taking an example.!

When we going to factorise an algebraic expression then we have to write it's factorised products. These factors may be number, algebraic variable or algebraic expression. For example,

→ x²-5x-6=0

→ x²-6x+x-6 = 0

→ x(x-6) + 1(x-6) = 0

→ (x+1)(x-6) = 0

→ x = -1 or x = 6

→ x = -1 or +6

There are many ways to factorise. But the most important way is middle term splitting method.

✴ Algebraic identities -

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto (A+B)^{2} \: = \: = A^{2} \: + \: 2AB \: + B^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto (A-B)^{2} \: = \: = A^{2} \: - \: 2AB \: + B^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto A^{2} \: - B^{2} \: = \: (A+B) \: (A-B)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto (A+B)^{2} \: = (A-B)^{2} \: +4AB}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto (A-B)^{2} \: = (A+B)^{2} \: -4AB}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto (A+B)^{3} \: = A^{3} + \: 3AB \: (A+B) \:+ B^{3}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto (A-B)^{3} \: = A^{3} - \: 3AB \: (A-B) \: + B^{3}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto A^{3} \: + B^{3} = \: (A+B) (A^{2} - AB + B^{2}}}}$

✴ Factorised identities -

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:+\;b)^{2}\; =\;a^{2}\:+\:b^{2}\:+\:2ab}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:-\:b)^{2}\;=\;a^{2}\:+\:b^{2}\:-\:2ab}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:+\:b\:+\:c)^{2}\;=\;a^{2}\:+\:b^{2}\:+\:c^{2}\:+\:2ab\:+\:2bc\:+\:2ac}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:+\;b)^{3}\;=\;a^{3}\:+\:b^{3}\:+\:3ab(a\:+\:b)}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto\;\;(a\:-\;b)^{3}\;=\;a^{3}\:-\:b^{3}\:-\:3ab(a\:-\:b)}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto \;\;(a+b)^{2} \: = \: a^{2} + 2ab + b^{2}}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto \;\;(a-b)^{2} \: = a^{2} - 2ab + b^{2}}\end{gathered}$

$\begin{gathered}\\\;\sf{\leadsto \;\;(a+b)(a-b) \: = \: a^{2} - b^{2}}\end{gathered}$