Question

the no. of equation that can be formed in for o ax^2 + bx + c tht has real roots ( a >= 2 and b<= 6 and a and b are positive numbers ) are?​

Answer 1

Answer:

The number of roots of a polynomial equation is equal to its degree. Hence, a quadratic equation has 2 roots. Let α and β be the roots of the general form of the quadratic equation :ax2 + bx + c = 0. We can write:

α = (-b-√b2-4ac)/2a and β = (-b+√b2-4ac)/2a

Here a, b, and c are real and rational. Hence, the nature of the roots α and β of equation ax2 + bx + c = 0 depends on the quantity or expression (b2 – 4ac) under the square root sign. We say this because the root of a negative number can’t be any real number. Say x2 = -1 is a quadratic equation. There is no real number whose square is negative. Therefore for this equation, there are no real number solutions.