What is the positive value of m for which the roots of the equation 12x2 mx 5 0 are in the ratio 3 2...........

Quantitative Aptitude (CDS) Quadratic Equations

Download Solution PDF

What is the positive value of m for which the roots of the equation 12x² + mx + 5 = 0 are in the ratio 3 : 2?

5√10

5√10 / 12

5/12

12/5

छोटे Courses बड़े Results

Master Quadratic Equations

Prepare through Micro-courses

Try Now

Explanation:

Let the two roots be 3x and 2x,
Let $\alpha$ =3x ?????? $\beta$ =2x, sum of root a+b = 3x + 2x = − m/ 12
=> 5 x = −m/12
=> m = -60x ------ (i)
Products of roots,
$\alpha$ $\beta$ =3x × 2x=5/12
=> 6x²= 5/12
=> x² = 5/72
=> x = ±√5/√72 = ±√5/6√2
Putting this value of x in (i), we get m = -60×(±√5/6√2)
Since we need positive value of m therefore
m = 60×(√5/6√2)=5√10