Question

if α and α + 1 are the roots of the equation x^2 - 7x + a = 0 find the value of a.

Answer 1

Answer:

Since, 4 is root of x

2

−7x+k=0

⇒4

2

−7×4+k=0

⇒16−28+k=0

⇒k=12

Step-by-step explanation:

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Answer 2

Sum of roots of any quadratic polynomial of the form

a'x² + bx + c = 0

= -b/a'

Here b = -7 and a' = 1

So sum of roots, α + α + 1 = 7

2α = 6

α = 3

So roots are 4 and 3

Product of roots = 4×3 = 12

Product of roots is c/a'

c = a and a' = 1

So a = 12