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

Answer:

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

Step-by-step 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 = $\frac{ - b}{a}$

       product of roots = $\frac{c}{a}$

So, 2 + 7 = $\frac{ - b}{a}$

Or, 2 × 7 =  $\frac{c}{a}$

I.e $\frac{ - b}{a}$  = 9     ,     $\frac{c}{a}$ = 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