Question

Find the discriminant of the quadratic equation 2x²-6x+3=0 and hence write the
nature of roots.​

Answer 1

Heya

hope it helps you....

Answer 2

⠀⠀⠀⠀⠀★ QUADRATIC EQUATIONS —

$\underline{\bf{\dag} \:\mathfrak{Discriminant \; Formula\: :}}$

$\star\boxed {\pink{\sf{ Discriminant = b^2 - 4ac }}}$

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⠀⠀⠀⠀⠀ Quadratic equation = 2x² - 6x + 3 = 0

where,

• a is coefficient of x² = 2

• b is coefficient of x = -6

• c is constant term = 3

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$:\implies \sf{ D = (-6)^2 - 4(2) \times 3 }\\\\:\implies \sf{ D = 36 - 4(2) \times 3 }\\\\:\implies \sf{ D = 36 - 8 \times 3 }\\\\:\implies \sf{ D = 36 - 24 }\\\\\underline {\boxed{\pink{ \mathrm {  Discriminant \:or\:D\:= 12\: }}}}\:\bf{\bigstar}$

$\rule{100px}{.3ex}$

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$\underline{\bf{\dag} \:\mathfrak{Finding\:Nature\;of\;Roots\: :}}$⠀⠀

• D (Discriminant) = 12

If,

• D > 0 (roots are unequal and real)

• D = 0 (roots are real and equal)

• D < 0 (roots are unequal and Imaginary)

$\rule{250px}{.3ex}$

Therefore,

As , We can see that ,

• 12 > 0 [ D > 0 (roots are unequal and real) ]

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  The\:roots\:are\:\bf{\:unequal \:and\: real }}}}$

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