Math, asked by Akshad07, 9 months ago

Form the quadratic equation if its roots are 1/2,-3/4

Answers

Answered by DarkBeats

30

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First Root = $\large{\frac{1}{2}}$

Which Means

➡️ $x=\frac{1}{2}$

➡️ $2x=1$

$\therefore$ Factor = 2x-1

Second Root = $\large{\frac{-3}{4}}$

Which means

➡️ $x=\frac{-3}{4}$

➡️ $4x=-3$

$\therefore$ Factor = 4x+3

Now on multiplying these Factors..

⚡ $(2x-1)(4x+3)$ ⚡

➡️ $8x^2+6x-4x-3$

➡️⭐ $\Large{\orange{8x^2+2x-3}}$ ⭐

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Answered by Aloi99

53

Given:-

•α= $\frac{1}{2}$

•β= $\frac{-3}{4}$

$\rule{200}{1}$

To Find:-

♦The Quadratic Equation using the Given details?

$\rule{200}{1}$

AnsWer:-

↓Quadratic Formula↓

→k[x²-(α+β)x+αβ]

→α+β= $\frac{1}{2}$ + $\frac{-3}{4}$

•Take LCM•

→α+β= $\frac{1×2}{2×2}$ + $\frac{-3}{4}$

→α+β= $\frac{-1}{4}$

→αβ= $\frac{1}{2}$ × $\frac{-3}{4}$

→αβ= $\frac{-3}{8}$

↑Using these Values in The Formula↑

→k[x²-( $\frac{-1}{4}$ x)+( $\frac{-3}{8}$ ) ]

★Let k=8★

→8[x²-( $\frac{-1}{4}$ x)+( $\frac{-3}{8}$ ) ]

→8x²-(-2x)+(-3)

→8x²+2x-3=quadratic Equation

$\rule{200}{2}$

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