Question

. Find the discriminant of the equation 3-5x+2-0 and hence write the nature
of its roots​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ 3x² - 5x + 2 = 0.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

⇒ D = (-5)² - 4(3)(2).

⇒ D = 25 - 24.

⇒ D = 1.

Nature of roots are real and equal : D = 0.

                                                                                                                           

MORE INFORMATION.

Nature of the roots 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

${\large{\pmb{\sf{\underline{Explaination...}}}}}$

★ As it's given that we have to find out the discriminant and the given equation is 3-5x+2=0 and we have to find out the nature of the root too.

${\large{\pmb{\sf{\underline{Required \; Solution...}}}}}$

${\small{\underline{\boxed{\sf{Discriminant \: = b^2-4ac}}}}} \\ \\ :\implies \sf Discriminant \: = b^2-4ac \\ \\ :\implies \sf Given \: that \: 3-5x+2=0 \\ \\ :\implies \sf Discriminant \: = (-5)^{2} - 4(3)(2) \\ \\ :\implies \sf Discriminant \: = (5)^{2} - 4(3)(2) \\ \\ :\implies \sf Discriminant \: = 5 \times 5 - 4(3)(2) \\ \\ :\implies \sf Discriminant = 25 - 4(3)(2) \\ \\ :\implies \sf Discriminant = 25 - 4(6) \\ \\ :\implies \sf Discriminant = 25 - 4 \times 6 \\ \\ :\implies \sf Discriminant = 25 - 24 \\ \\ :\implies \sf Discriminant = 1$

Henceforth, discriminant is 1 and the nature of the root is Real and Equal.

${\large{\pmb{\sf{\underline{Additional \; Knowledge...}}}}}$

Some knowledge about Quadratic Equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ Discriminant is given by b²-4ac

• Discriminant tell us about there are solution of a quadratic equation as no solution, one solution and two solutions.

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

★ D > 0 then roots are real and distinct.

★ D = 0 then roots are real and equal.

★ D < 0 then roots are imaginary.

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