class 9 - 2x^2+11√2x+24
Answers
Question:
Find the roots of the quadratic equation by factorization.
2x² + 11 √2 x + 24 = 0
Answer:
The roots of the given equation are
x = - 3 √2 / 2 and x = - 4 √2.
Step-by-step-explanation:
The given quadratic equation is
2x² + 11 √2 x + 24 = 0.
We have to solve this equation with factorization method.
We need two factors of 48x² such that their sum is 11 √2 x.
These both factors will have √2 in common. And the product of √2 with √2 is 2. So, the product of two numbers with √2 will be ( 48 / 2 ) which is 24.
The factors of 24 with sum 11 are 8 and 3.
So, the required two factors of 48x² are 8 √2 x and 3 √2 x.
Now,
2x² + 11 √2 x + 24 = 0
⇒ 2x² + 3 √2 x + 8 √2 x + 24 = 0
⇒ √2 x ( √2 x + 3 ) + 8 ( √2 x + 3 ) = 0
⇒ ( √2 x + 3 ) ( √2 x + 8 ) = 0
⇒ ( √2 x + 3 ) = 0 OR ( √2 x + 8 ) = 0
⇒ √2 x + 3 = 0 OR √2 x + 8 = 0
⇒ √2 x = - 3 OR √2 x = - 8
⇒ x = - 3 / √2 OR x = - 8 / √2
⇒ x = - 3 / √2 * ( √2 / √2 ) OR x = - 8 / √2 * ( √2 / √2 )
⇒ x = - 3 √2 / 2 OR x = - 8 √2 / 2
⇒ x = - 3 √2 / 2 OR x = - 4 √2
∴ The roots of the given equation are
x = - 3 √2 / 2 and x = - 4 √2.