Question

Difference between the roots of a quadratic equation x2 - 4x + c = 0 is 6. Then the value of c is​

Answer 1

Solution

The value of c is - 5

Given Polynomial,

p(x) = x² - 4x + c

The difference of the zeros is 6

Let m and n be the zeros of the above polynomial

Sum of Zeros

m + n = - (- 4)

→ m + n = 4 ------------(1)

Also,

m - n = 6 ------------(2)

Adding equations (1) and (2),

→ 2m = 10

→ m = 5

Putting m = 5 in (1),we get :

n = - 1

Now,

Product of Zeros = c

→ (-1)(5) = c

→ c = - 5

Answer 2

$\huge\bold{Question}$

Difference between the roots of a quadratic equation x2 - 4x + c = 0 is 6. Then the value of c is _____ ?

$\huge\bold{Answer}$

So, according to the question , we have

→ P(x) = x² - 4x + c

And, The difference of the zeros is 6

Let " m" and " n " be the zeros of the given polynomial, given in question

Hence, the Sum of Zeros are

→ m + n = - (- 4)

→ m + n = 4 _____________________(¡)

And, 2nd are

→m - n = 6 _____________________(¡¡)

Simply by adding the equations (¡) and (¡¡) we get :-

→ m + m + n - n = 4 + 6

→ 2 m = 10

→ m = 5

Now , by substituting the valu of " m " in eqn (¡)

→ n = - 1

Hence , the Product of Zeros = c

→ (-1) × (5) = c

→ c = - 5

Hence , the required value of “ c ” is - 5