Question

solve the following quadratic equation by factorization method 5t2-12t-20=0​

Answer 1

SolutioN :

We have, Equation.

$\tt \dagger \: \: \: \: \: 5 {t}^{2} - 12t - 20 =0 .$

✡ Compare With General Equation.

$\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c =0 .$

Where as,

• a = 5.
• b = - 12.
• c = - 20.

☛ Let's Find Roots :

$\tt \dagger \: \: \: \: \:\fbox{ D = b^2-4ac.}$

Where as,

• D Discriminate.

$\tt : \implies D = { \big(- 12 \big)}^{2} - 4 \times 5 \times - 20$

$\tt : \implies D = 144 + 400.$

$\tt : \implies D = 544 .$

Now,

✎ We have, Quadratic Formula.

$\tt \dagger \: \: \: \: \:\fbox{ x = \dfrac{-b\pm \sqrt{ {b}^{2}-4ac } }{2a} }$

$\tt : \implies x = \dfrac{12\pm \sqrt{ D} }{2 \times 5}$

$\tt : \implies x = \dfrac{12\pm \sqrt{ 544} }{10}$

♢ Therefore, the value Of x is 12 ± √544 /10.