Question

complete the following activity to determine the nature of the root of the quadratic equation 2x2 - 5x+3=0.​

Answer 1

Step-by-step explanation:

Giventhat...Giventhat...

{\green{\bigstar}}★ A quadratic equation is given as {\red{\sf{2x^{2} - 5x + 3 = 0}}}2x2−5x+3=0

{\large{\pmb{\sf{\underline{To \; find...}}}}}Tofind...Tofind...

{\green{\bigstar}}★ Determine the nature of the root of the given quadratic equation.

{\large{\pmb{\sf{\underline{Solution...}}}}}Solution...Solution...

{\green{\bigstar}}★ The nature of the root of the quadratic equation {\red{\sf{2x^{2} - 5x + 3 = 0}}}2x2−5x+3=0 is {\red{\sf{Real}}}Real and {\red{\sf{Equal}}}Equal

{\large{\pmb{\sf{\underline{Knowledge...}}}}}Knowledge...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

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━

{\large{\pmb{\sf{\underline{Using \; concepts...}}}}}Usingconcepts...Usingconcepts...

{\red{\bigstar}}★ Discriminant is given by the given:

{\small{\underline{\boxed{\sf{b^{2} - 4ac}}}}}b2−4ac

{\large{\pmb{\sf{\underline{Full \; Solution...}}}}}FullSolution...FullSolution...

{\small{\underline{\boxed{\sf{b^{2} - 4ac}}}}}b2−4ac

{\sf{:\implies b^{2} - 4ac}}:⟹b2−4ac

{\sf{:\implies Given \: that \: = 2x^{2} - 5x + 3 = 0}}:⟹Giventhat=2x2−5x+3=0

{\sf{:\implies (-5)^{2} - 4(2)(3)}}:⟹(−5)2−4(2)(3)

{\sf{:\implies -5 \times -5 - 4(2)(3)}}:⟹−5×−5−4(2)(3)

{\sf{:\implies 5 \times 5 - 4(2)(3)}}:⟹5×5−4(2)(3)

{\sf{:\implies 25 - 4(2)(3)}}:⟹25−4(2)(3)

{\sf{:\implies 25 - 4(6)}}:⟹25−4(6)

{\sf{:\implies 25 - 4 \times 6}}:⟹25−4×6

{\sf{:\implies 25 - 24}}:⟹25−24

{\sf{:\implies 1}}:⟹1

Henceforth, the discriminant is 1. Therefore, the nature of the root of the given quadratic equation is Equal and Real.

Answer 2

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

${\green{\bigstar}}$ A quadratic equation is given as ${\red{\sf{2x^{2} - 5x + 3 = 0}}}$

${\large{\pmb{\sf{\underline{To \; find...}}}}}$

${\green{\bigstar}}$ Determine the nature of the root of the given quadratic equation.

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

${\green{\bigstar}}$ The nature of the root of the quadratic equation ${\red{\sf{2x^{2} - 5x + 3 = 0}}}$ is ${\red{\sf{Real}}}$ and ${\red{\sf{Equal}}}$

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

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

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━

${\large{\pmb{\sf{\underline{Using \; concepts...}}}}}$

${\red{\bigstar}}$ Discriminant is given by the given:

${\small{\underline{\boxed{\sf{b^{2} - 4ac}}}}}$

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

${\small{\underline{\boxed{\sf{b^{2} - 4ac}}}}}$

${\sf{:\implies b^{2} - 4ac}}$

${\sf{:\implies Given \: that \: = 2x^{2} - 5x + 3 = 0}}$

${\sf{:\implies (-5)^{2} - 4(2)(3)}}$

${\sf{:\implies -5 \times -5 - 4(2)(3)}}$

${\sf{:\implies 5 \times 5 - 4(2)(3)}}$

${\sf{:\implies 25 - 4(2)(3)}}$

${\sf{:\implies 25 - 4(6)}}$

${\sf{:\implies 25 - 4 \times 6}}$

${\sf{:\implies 25 - 24}}$

${\sf{:\implies 1}}$

Henceforth, the discriminant is 1. Therefore, the nature of the root of the given quadratic equation is Equal and Real.