Question

find the discriminant of quadratic equation root 5 x square - 7 x + 2 root 5 equal to zero​

Answer 1

Question:

Find the discriminant of the quadratic equation

√5x² - 7x + 2√5 = 0.

Answer:

D = 9

Note:

• An equation of degree 2 is know as quadratic equation .

• Roots of an equation is defined as the possible values of the unknown (variable) for which the equation is satisfied.

• The maximum number of roots of an equation will be equal to its degree.

• A quadratic equation has atmost two roots.

• The general form of a quadratic equation is given as , ax² + bx + c = 0 .

• The discriminant of the quadratic equation is given as , D = b² - 4ac .

• If D = 0 , then the quadratic equation would have real and equal roots .

• If D > 0 , then the quadratic equation would have real and distinct roots .

• If D < 0 , then the quadratic equation would have imaginary roots .

Solution:

The given quadratic equation is ;

√5x² - 7x + 2√5

Clearly , we have ;

a = √5

b = -7

c = 2√5

We know that,

The discriminant (D) is given by b² - 4ac.

Thus,

=> D = (-7)² - 4•√5•2√5

=> D = 49 - 40

=> D = 9

Hence,

The required value of discriminant is 9.

Answer 2

$\huge{\boxed{\red{\star\;Answer}}}$

$\large{\underline{\blue{\star\;Note}}}$

$\boxed{\purple{Given\;equation\;\sqrt{5}x^{2}-7x+2\sqrt{5}=0}}$

$\large{\underline{\green{\star\;Discriminent}}}$

• If $ax^{2}+bx+c=0$ is a quadratic equation then

• Discriminent is defined as follows

• $D=\sqrt{b^{2}-4ac}$

• If D > 0 , roots exist and they are real and distinct
• If D = 0 , roots exist and they are equal
• If D < 0 , roots are imaginery

$\underline{\purple{Calculating\;D\;of\;given\; equation\;\sqrt{5}x^{2}-7x+2\sqrt{5}=0}}$

• $D\;=\sqrt{b^{2}-4ac}$
• Here,
• a = √5
• b = -7
• c = $2\sqrt{5}$

• $D=\sqrt{b^{2}-4ac}$

• $D=\sqrt{{-7}^{2}-4(\sqrt{5})(2\sqrt{5}}$

• $D=\sqrt{49-40}$

$\large{\boxed{\red{The\;value\;D\;is\;3}}}$