Question

If a quadratic equation ax Square + bx + c = 0, where a, b, c are real numbers and a is not equal to zero, has real and equal roots then​

Answer 1

Step-by-step explanation:

If a quadratic equation ax Square + bx + c = 0, where a, b, c are real numbers and a is not equal to zero, has real and equal roots then

${b}^{2} - 4ac = 0$

If a quadratic equation ax Square + bx + c = 0, where a, b, c are real numbers and a is not equal to zero, has real and unequal roots then

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

If a quadratic equation ax Square + bx + c = 0, where a, b, c are real numbers and a is not equal to zero, has non-real roots then

${b}^{2} - 4ac \leq 0$

Answer 2

Answer:

Step-by-step explanation:

Given equation

ax^2+bx+c=0

Determinant of the equation should be positive for its roots to be real

i.e, b^2 −4ac>0

 Because it reduces determinant to b^2 which is always positive.

When a, b, and c are real numbers, a ≠ 0 and the determinant is a perfect square but if any one of a or b is irrational then the roots of the quadratic equation ax2 + bx + c = 0 are irrational.

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