Question
ax2 + 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 ax2 + 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 ax2 + 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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