Question

y2+24y+144=0
please someone find me the root of this quadratic equation ​

Answer 1

y² + 24y + 144 = 0

=> y² + (12y + 12y) + 144 = 0

=> y² + 12y + 12y + 144 = 0

=> y(y + 12) + 12(y + 12) = 0

=> (y + 12) (y + 12)

=> y = -12 and y = -12

hence, the roots of the polynomial are -12 and -12

Answer 2

$\bf{\huge{\underline{\underline{\boxed{\mathfrak{\blue{Answer:}}}}}}}$

Given quadratic equation:

y² + 24y + 144

Solve the equation by factorization method. We would split the middle term of the equation (24y) in such way that we get two numbers whose product should be 144 and sum should be equal to 24.

Let's hit up!

Solution:

y² + 24y + 144 = 0

y² + 12y + 12y + 144 = 0 $\bf\underbrace{Splitting\:the\:middle \:term}$

y ( y + 12) 12 ( y + 12) = 0 $\bf\underbrace{Finding\:the \:factors}$

(y+12) (y + 12) = 0

y + 12 = 0 OR y + 12 = 0

y = -12 OR y = -12

•°• the roots of the quadratic equation are -12 & -12.

$\bf{\large{\boxed{\rm{\red{Verification}}}}}$

Put y = - 12 in the given quadratic equation : y² + 24y + 144 = 0

-12² + 24 × -12 + 144 = 0

144 -288 + 144 = 0

144 + 144 - 288 = 0

288 - 288 = 0

0 = 0

•°• LHS = RHS

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