Question

The solution to a quadric equation are x=2 and x=7. If k is a nonzero constant which of the following must be equal to the quadratic equation

Answer 1

The quadratic equation form is x² - 9 x + 14 = 0

Explanation:

Given in the question as ,

The solution of quadratic equation are x = 2 and x = 7

The constant K is a non-zero number

Now , let the quadratic equation be , ax² + bx + c = 0

And sum of roots =
`( - b)/(a)`

product of roots =
`(c)/(a)`

So, 2 + 7 =
`( - b)/(a)`

Or, 2 × 7 =
`(c)/(a)`

I.e
`( - b)/(a)` = 9 ,
`(c)/(a)` = 14

Or, b = - 9 a And c = 14 a

Put this value of b and c in standard form of quadratic equation

I.e ax² + bx + c = 0

Or, ax² - 9 ax + 14 a = 0

Or , a ( x² - 9 x + 14 ) = 0

∴ a = 0 And x² - 9 x + 14 = 0

Hence , The quadratic equation form is x² - 9 x + 14 = 0 Answer