Question

If one root of the quadratic equation 2x² + 12x - m = 0 is 1.5 times the other root, then find the value of m .
---Explain in details please ---
a) -27/8
b) -432/25
c) -288/25
d) -16​

Answer 1

Answer:

b) -432/25

Step-by-step explanation:

If one root is k then other root is 1.5k

So, sum of roots -

k + 1.5k = -(12/2) = -6

=> 2.5k = -6

=> k = -6/2.5 = -2.4

So , roots are -2.4 & -3.6

Now , product of root

or -2.4×(-3.6) = - m/2

or m = -17.28 = -432/25

Ans: m = -432/25

Answer 2

Given: quadratic equation 2x² + 12x - m = 0, one root is 1.5 times the other root

To find: The value of m

Solution: The general equation of quadratic equation be ax^2+bx+ c=0

here the product pf roots = c/a

the sum of roots = -b/a

Now according to the given quadratic equation, we can say that

x1+x2= -6

x1x2= - m/2

where x1 and x2 are roots of the equation

also, we are given that x1= 1.5x2

solving these equation we will get

x2= -6/2.5= -2.4= - 12/5

m= -2×1.5x2× x2= -3 (x2^2)= -3× 144/5= -432/24

Therefore, the value of m will be b) -432/25.