Question

the value of k,so that the sum and product of the roots of 2x²+(k-3)x+3k-5=0 are equal is

Answer 1

Answer:

2

Step-by-step explanation:

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Answer 2

Value of k is 2, if sum and product of roots are equal.

Given:

• A quadratic equation.
• $2 {x}^{2} + (k - 3)x + 3k - 5 = 0$

To find:

• Find value of k, if sum and product of roots are equal.

Solution:

Concept to be used:

A standard quadratic equation is given by

$\bf a {x}^{2} + bx + c = 0$, where a≠0.

If $\alpha \: and \: \beta$ are roots of this equation.

There is a relationship between zeros of quadratic equation and it's coefficients.

1. Sum of zeros; $\alpha + \beta = \frac{ - b}{a}$
2. Product of zeros; $\alpha \beta = \frac{c}{a}$

Step 1:

Compare the given equation with standard equation.

It is clear that,

$a = 2$

$b = k - 3$

and

$c = 3k - 5$

Let $\alpha \: and \: \beta$ are the zeros, then according to relationship.

$\alpha + \beta = \frac{ - (k - 3)}{2}...eq1$

and

$\alpha \beta = \frac{3k - 5}{2} ...eq2$

Step 2:

Compare eq1 and eq2.

As, it is given in the question that, if sum and product of roots are equal.

So,

$\frac{ - (k - 3)}{2} = \frac{3k - 5}{2}$

or

$- k + 3 = 3k - 5$

or

$- k - 3k = - 5 - 3$

or

$- 4k = - 8$

or

$4k = 8$

or

$k = \frac{8}{4}$

or

$\bf \red{k = 2}$

Thus,

Value of k is 2, if sum and product of roots are equal.

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