In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in the coefficient of first-degree term and finds -9 and -1 for roots. The correct equation is

Step-by-step solution

Let correct equation is a x^2+b x+c=0 According to first student, equation is: a x^2+b x+c₁=0 and roots are 8 and 2 8+2= -b a b a =-10 Quadratic equation according to second student ax ^2+ b ₁ x + c =0 and roots are -9 and -1 (-9) (-1)= c a c a =9 Putting value in original equation aligned & x^2+ b a x+ c a =0 & x^2-10 x+9=0 aligned