Question

If alpha and beta equation 2 X square-3x+5 =0 ke mul ho to alpha square beta+Alpha beta square ka man gyat karo

Answer 1

EXPLANATION.

α,β are the roots of the equation,

⇒ F(x) = 2x² - 3x + 5 = 0.

As we know that,

Sum of zeroes of quadratic equation,

⇒ α + β = -b/a.

⇒ α + β = -(-3)/2 = 3/2.

Products of zeroes of quadratic equation,

⇒ αβ = c/a.

⇒ αβ = 5/2.

To find the value of,

(1) = α²β + αβ².

⇒ αβ(α + β).

Put the value in this equation, we get.

⇒ 5/2(3/2).

⇒ 15/4.

                                                                                                                       

MORE INFORMATION.

Nature of the factors of the quadratic expression,

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.

Answer 2

Answer:

Solution :-

F(x) = 2x² - 3x + 5 = 0

We know that

Sum of zeroes Quardtic equation

$\sf \: \alpha + \beta \: = \dfrac{ - b}{a}$

Here,

b = -3

a = 2

$\sf \: \alpha + \beta = \dfrac{ - ( - 3)}{ 2}$

${ \rm \alpha + \beta = \dfrac{3}{2} }$

$\blue{ \rm \alpha + \beta = \dfrac{3}{2} }$

Now,

Product of zeroes

$\sf \: \alpha \beta = \dfrac{c}{a}$

$\sf \: \alpha \beta = \dfrac{5}{2}$

$\blue{ \rm \: \alpha \beta = \frac{5}{2}}$

Now,

Value of

$\sf \: \alpha {}^{2} \beta + { \alpha \beta }^{2}$

$\sf \: \alpha \beta ( \alpha + \beta )$

Now,

$\sf \: \dfrac{5}{2} \times \dfrac{3}{2}$

$\sf \: \dfrac{15}{4}$

$\rm \blue{ \dfrac{15}{4}}$