Question

If the roots of the quadratic equation ax + bx+c= 0 (a is not 0) are REAL, then​

Answer 1

Answer:

We know that α and β are the roots of the general form of the quadratic equation ax22 + bx + c = 0 (a ≠ 0) .................... (i) then we get

α = −b−b2−4ac√2a−b−b2−4ac2a and β = −b+b2−4ac√2a−b+b2−4ac2a

Here a, b and c are real and rational.

Then, the nature of the roots α and β of equation ax22 + bx + c = 0 depends on the quantity or expression i.e., (b22 - 4ac) under the square root sign.

Thus the expression (b22 - 4ac) is called the discriminant of the quadratic equation ax22 + bx + c = 0.

$\blue{We know that α and β are the roots of the general form of the quadratic equation ax22 + bx + c = 0 (a ≠ 0) .................... (i) then we get</p><p>α = −b−b2−4ac√2a−b−b2−4ac2a and β = −b+b2−4ac√2a−b+b2−4ac2a</p><p>Here a, b and c are real and rational.</p><p>Then, the nature of the roots α and β of equation ax22 + bx + c = 0 depends on the quantity or expression i.e., (b22 - 4ac) under the square root sign.</p><p>Thus the expression (b22 - 4ac) is called the discriminant of the quadratic equation ax22 + bx + c = 0.</p><p>}$

Answer 2

Answer:

Your question haa a mistake. Since we all know that quadratic equation is in the form of: ax^2 + bx + c = 0

• if a is not 0 then the roots of quadratic equation may or may not be real

For example:

x^2 + 9x + 14 = 0

Here you can observe the a which is = 1 and 1 is greater than zero.

Step-by-step explanation:

First of all the quadratic equation is in the form of:

ax^2 + bx + c = 0

x^2 + 9x + 14 = 0

x^2 + 2x + 7x + 14 = 0

x (x+2) + 7 (x+2) = 0

either (x+2)=0 or (x+7) = p

therefore x= -2 , -7