Question

if one root of the quadratic equation 2x saure + 12x-m=0 is three times that are the root then find the value of m?
1)-16
2)-288/25
3)-27/8
4)-432/25
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Answer 1

Step-by-step explanation:

One of the roots of quadratic equation 2x2 + x – 300 = 0 is (1) 16 (2) 18 (3) 15 (4) 12. 2.

Option 4 is correct (12)Given:2x²+ x - 300 = 02x² - 24x +25x -300= 02x(x-12) +25(x-12)=

Answer 2

The value of 'm' is - 27/2  

Given:

One root of the quadratic equation 2x² + 12x-m = 0 is 3 times that the root  

To find:

Find the value of m

Solution:

 

The quadratic equation is 2x² + 12x-m = 0  

One root of the quadratic equation is 3 times that of the root  

Let 'x' be the one root and 3x be the other root

Sum of the roots, x + 3x = 4x

From the equation,

the sum of the roots = -12/2 = - 6

=> 4x = - 6

=> x = - 6/4

=> x = -3/2

Product of the roots = x(3x) = 3x²  

From the equation,

the product of roots = - m/2

=> 3x² = - m/2  

=> 6(-3/2)² = - m

=> 6(9/4) = - m

=> m = - 27/2        

Therefore,

The value of 'm' is - 27/2        

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