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 = [tex]\frac{ - b}{a}[/tex]
product of roots = [tex]\frac{c}{a}[/tex]
So, 2 + 7 = [tex]\frac{ - b}{a}[/tex]
Or, 2 × 7 = [tex]\frac{c}{a}[/tex]
I.e [tex]\frac{ - b}{a}[/tex] = 9 , [tex]\frac{c}{a}[/tex] = 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
