Question

# ax^{2} + bx + c = 0 has real and distinct roots null. Further a > 0, b < 0 and c < 0, then –

Hint:

### The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. Here we have given ax^{2} + bx + c = 0 has real and distinct roots null. We have to find the correct condition.

## The correct answer is:

### A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two. It takes the following form:

ax² + bx + c = 0

where a, b, and c are constant terms and x is the unknown variable.

Now we have given a > 0, b < 0 and c < 0, the equation is ax^{2} + bx + c = 0.

Let the roots be α and β, where β>α, then:

α + β = -b/a $>0$ as $a>0,b<0$.

αβ = c/a as $a>0,c<0$.

Now that the roots are of opposite signs, so β > 0 and α < 0.

So: $α∣β$ as α$β>0$.

So therefore: 0 < ∣α∣ < β

Here we used the concept of quadratic equations and solved the problem. The concept of sum of roots and product of roots was also used here. Therefore, 0 < ∣α∣ < β.

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