Question

1. Find the nature of roots of the quadratic equation 2x² – 4x + 3 = 0.​

Answer 1

given : f(x) = 2x²-4x+3=0

to find the nature of roots

a= 2, b = -4 and c = 3

D = b²-4ac = (-4)² - 4(2)(3)

=> 16 - 24

=> -8

therefore as D < 0, roots are not real or roots are imaginary

Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{\red{Solution}}}}}}$

$\Large{\underline{\mathfrak{\bf{\orange{Given}}}}}$

• Equation, 2x² - 4x + 3 = 0

$\Large{\underline{\mathfrak{\bf{\orange{Find}}}}}$

• Nature of Roots of given equation

$\Large{\underline{\underline{\mathfrak{\bf{\red{Explanation}}}}}}$

We Find, Nature of Roots, by Discriminant

1. B² - 4AC = 0 ----> Roots are equal ,real & rational
2. B² - 4AC > 0 , and also a perfect square --> Roots are real , distinct & rational
3. B² - 4AC >0 ,but not a perfect square -----> Roots are real, distinct & irrational
4. B² - 4AC <0 , ---> Roots are imaginary
5. B² - 4AC >= 0 ---> Roots are real

Now, Calculate Discriminant,

Here

• B = -4
• A = 2
• C = 3

==> B² - 4AC

Keep All above values

= (-4)² - 4 * 2 * 3

= 16 - 24

= -8 < 0

Discriminant is negative

Hence

• Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary .

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