If b2-4ac≥0 then the roots of quadratic equation ax2+bx+c=0 is

It is given that for the equation ax2+bx+c=0 , b2-4ac≥0.Here are the relations between roots and discriminant● When roots are non-real, the discriminant is less than 0● When roots are real and equal, the discriminant is equal to 0● When the roots real and unequal the discriminant is greater than 0If b2-4ac≥0 then the roots are real and distinct,Let the roots be α and β.We know that,α+β=-ba…..(1)αβ=ca…..(2)We can write that,(α-β)2=(α+β)2-4αβ Substituting the values of α+β and αβ in the above equation,α-β=b2-4aca …… (3)Adding equation 1 and 3, we get,α=-b±b2-4ac2a Hence, by using quadratic formula, we get the roots as -b±b2-4ac2a Hence, option 4 is correct.

If b2-4ac≥0 then the roots of quadratic equation ax2+bx+c=0 is

It is given that for the equation ax2+bx+c=0 , b2-4ac≥0.Here are the relations between roots and discriminant● When roots are non-real, the discriminant is less than 0● When roots are real and equal, the discriminant is equal to 0● When the roots real and unequal the discriminant is greater than 0If b2-4ac≥0 then the roots are real and distinct,Let the roots be α and β.We know that,α+β=-ba…..(1)αβ=ca…..(2)We can write that,(α-β)2=(α+β)2-4αβ Substituting the values of α+β and αβ in the above equation,α-β=b2-4aca …… (3)Adding equation 1 and 3, we get,α=-b±b2-4ac2a Hence, by using quadratic formula, we get the roots as -b±b2-4ac2a Hence, option 4 is correct.

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If $b^{2} - 4 ac \geq 0$ then the roots of quadratic equation $a x^{2} + bx + c = 0$ is

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\frac{b}{2 a} + \frac{\sqrt{b^{2} - 4 ac}}{2 a}

- \frac{b}{2 a} - \frac{\sqrt{b^{2} + 4 ac}}{2 a}

\frac{b}{2 a} \pm \frac{\sqrt{b^{2} + 4 ac}}{2 a}

- \frac{b}{2 a} \pm \frac{\sqrt{b^{2} - 4 ac}}{2 a}

answer is D.

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Detailed Solution

It is given that for the equation

a x^{2} + bx + c = 0

b^{2} - 4 ac \geq 0 .

Here are the relations between roots and discriminant
●       When roots are non-real, the discriminant is less than 0
●       When roots are real and equal, the discriminant is equal to 0
●       When the roots real and unequal the discriminant is greater than 0
If