Question

If α and β are the roots of the equation ax2+bx+c=0,αβ=4ax2+bx+c=0,αβ=4 and a,b,,c are in A. P then α+β=

Answer 1

Considering the sum and the product of the roots of the quadratic equation, it is found that the numeric value of the expression is given as follows:

$\alpha + \beta = -2.5$

What are the sum and the product of the roots of a quadratic equation?

A quadratic equation is defined as follows:

$y = ax^2 + bx + c, a \neq 0$

The roots of the equation are given as follows:

$\alpha, \beta$

The sum of the roots is given as follows:

$\alpha + \beta = -\frac{b}{a}$

The product of the roots is given as follows:

$\alpha\beta = \frac{c}{a}$

In the context of this problem, the product is of 4, as $\alpha\beta = 4$ hence:

c/a = 4

c = 4a.

The coefficients are in an arithmetic progression, hence:

• b = a + d. (d is the common difference of the sequence).

• c = a + 2d.

We have that c = 4a, hence:

4a = a + 2d

2d = 3a

d = 1.5a.

Hence coefficient b is calculated as follows:

b = a + d = a + 1.5a = 2.5a.

Then the sum of the roots is given as follows:

$\alpha + \beta = -\frac{b}{a} = -\frac{2.5a}{a} = -2.5$

More can be learned about quadratic equations at brainly.com/question/24737967

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