Question

Find the discriminate of 2x² -4x+3=0 and discuss the nature of roots

Answer 1

Question :-

Find the discriminate of 2x²- 4x +3 = 0 and discuss the nature of roots .

Answer :-

→ Discriminate = -8

→ Nature - imaginary roots .

To Find :-

→ Discriminate and nature of roots .

Used formula :-

• Discriminate (D) = b² - 4ac

If

• D > 0 ( real roots and unequal roots )

• D ≥ 0( real and equal roots )

• D ≤ 0 ( imaginary roots )

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Explanation :-

We have

→ 2x² - 4x +3 = 0

compare with general Quadratic equation ax² +bx + c = 0

after comparing we get,

→ a = 2 , b = -4 and c = 3

Now ,

• Discriminate (D)= b² - 4ac

→ D = (-4)² - 4 × 2 × 3

→ D = 16 - 24

→ D = -8

if we need to discuss about nature of roots then always try to make it a perfect square .

here, D < 0

hence the roots of this Quadratic are imaginary .

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Now if we need to find that how these roots are imaginary then ,

now find roots of this equation ,

here we will use Shree dharacharya formula for finding roots .

i.e,

$\rightarrow \sf{x = \frac{ \purple{ -b + \sqrt{d}} }{ \green{2a}} \: or \: \frac{ \red{- b - \sqrt{d} }}{ \purple{2a}} }$

put value of a ,b and c ( given above ↑)

$\rightarrow \sf{x = \frac{ \purple{ - ( - 4) }+ \red{ \sqrt{ - 8}} }{ \green{2 \times 2}} \: or \: \frac{ \blue{ - ( - 4)} - \sqrt{ - 8} }{ \green{2 \times 2}} } \\ \\ \rightarrow \sf{ x = \frac{ \red{4 + 2 \sqrt{ - 2} }}{4} \: or \: \frac{ \green{4 - 2 \sqrt{ - 2} }}{ \blue{4}} } \:$

there roots are imaginary because inside square root get negative sign .

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