Question

Find the value of the discriminant of the quadratic equation 2x2 - 6x+4=0 and hence write the nature of the roots.
(pls answer you will be marked brainliest)​

Answer 1

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

★ It is given that we have to find the value of the discriminant of the quadratic equation ${\red{\sf{2x^{2}-6x+4=0}}}$ and hence write the nature of the roots. A formula is given below, we have to use this formula to find the solution for this question.

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

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

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

${\sf{:\implies D \: = (-6)^{2} - 4(2)(4)}}$

${\sf{:\implies D \: = (-6)^{2} - 4(8)}}$

${\sf{:\implies D \: = (-6)^{2} - 32}}$

${\sf{:\implies D \: = -6 \times -6 - 32}}$

${\sf{:\implies D \: = 6 \times 6 - 32}}$

${\sf{:\implies D \: = 36-32}}$

${\sf{:\implies D \: = 4}}$

${\sf{:\implies Discriminant \: = 4}}$

${\sf{:\implies 4 \: is \: greater \: than \: 0}}$

Therefore, distinct real(different and real) roots exist for this given equation.

${\pmb{\sf{\underline{Additional \; knowledge...}}}}$

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

★ A quadratic equation have 2 roots

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

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