Maths-
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Question

ax2 + bx + c = 0 has real and distinct roots null. Further a > 0, b < 0 and c < 0, then –

  1. 0 less than beta less than vertical line alpha vertical line    
  2. 0 less than vertical line alpha vertical line less than beta
  3. alpha plus beta less than 0
  4. open vertical bar alpha close vertical bar plus open vertical bar beta close vertical bar equals open vertical bar fraction numerator b over denominator a end fraction close vertical bar    

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: 0 less than vertical line alpha vertical line less than beta


    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 00.
    αβ = c/a as 00.
    Now that the roots are of opposite signs, so β > 0 and α < 0.
    So: α∣ β as α β 0.
    So therefore: 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, α∣ < β.

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