Question

find the nature of roots of quadratic equation 3 x square - 4 x + 4 equal to zero

Answer 1

${\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}}$

$\underline{\sf{\red{Given}}}$

⠀⠀⠀⠀⠀• Quadratic equation 3x²-4x+4

$\underline{\sf{\red{Answer}}}$

⠀⠀⠀⠀⠀• -32<0

$\underline{\sf{\red{To\: Calculate}}}$

⠀⠀⠀⠀⠀• Nature of the roots

$\underline{\sf{\red{Explanation}}}$

Given Quadratic equation ☞ 3x²-4x+4 =0

This is of the form ax²+bx+c=0

Where

a = 3

b = -4

c = 4

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀${\boxed{\red{\tt{D= b²-4ac }}}}$

putting values,

➛ $\underline{\sf{\red{D= b²-4ac}}}$

➛(-4)²-4×3×4

➛ 16- 48

➛ -32

${\boxed{\red{\tt{-32<0 }}}}$

${\huge{\underline{\underline{\sf{\blue{Hence }}}}}}$

⠀⠀⠀⠀⠀• The Given eq. has no real roots.

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⠀⠀⠀⠀⠀${\boxed{\blue{\tt{Additional\: information}}}}$

Case1

$\underline{\sf{\red{When D>0}}}$

In this case , The roots are real and distinct

Case2

$\underline{\sf{\red{When D=0}}}$

In this case , The roots are real and equal

Case 3

$\underline{\sf{\red{When D<0}}}$

In this case, The roots are imaginary, and we say that the Given equation has no real roots.

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