Question

If one root of the quadratic equation 8x2 - 28x + y = 0
is six times the other, then find the value of y​

Answer 1

Answer:

guru. (33) Nambiar would, from now in, care for her

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Answer 2

Step-by-step explanation:

Given :-

One root of the quadratic equation

8x^2-28x+y = 0 is six times the other .

To find :-

Find the value of y ?

Solution:-

Given that

The Quadratic equation = P(x) = 8x^2-28x+y = 0

On Comparing this with the standard quadratic equation ax^2+bx+c = 0

a = 8

b= -28

c= y

Let the other root be A

Then the one of the roots = 6 times to the other

=> 6A

The roots are 6A and A

We know that

Sum of the roots = -b/a

=> 6A+A = -(-28)/8

=> 7A = 28/8

=> A = 28/(8×7)

=> A= 28/56

=> A = 1/2----------(1)

and 6A = 6(1/2)

=> 6/2

=> 3

The roots are 3 and 1/2

Product of the roots = c/a

=> (6A)(A) = y/8

=> 6A^2 = y/8

=> 6(1/2)^2 = y/8 (from (1))

=> 6(1/4) = y/8

=> 6/4 = y/8

=> 3/2 = y/8

On applying cross multiplication then

=> 2×y = 3×8

=>2y = 24

=> y = 24/2

=> y = 12

Therefore,y = 12

Answer:-

The value of y for the given problem is 12

Used formulae:-

• The standard quadratic equation is ax^2+bx+c = 0

• Sum of the roots = -b/a

• Product of the roots = c/a