Determine the nature of roots of the following quadratic equation:-
√3 x² - 5x + 7√3 = 0
Answers
Answer: if x = 3 is a root of equation kx2 – 10x + 3 = 0 ... Solve the following quadratic equations by factorisation. (1) x2 ... (7) √2x2+7x+5√2=0 ... (8) 3x2-2√6x+2=0 ... 3: Determine the nature of roots of the following quadratic equations.
Step-by-step explanation:
Solution
Given equation :-
√3x² - 5x + 7√3 = 0
Compare to
ax² + bx +c = 0
So
a = √3 , b = -5 and c = 7√3
To find the nature of root find Discriminant
Discriminant(D) = b² - 4ac
⇒ D = (-5)² - 4 × √3 ×7√3
⇒D = 25 - 4 × 21
⇒D = 25 - 84
⇒D = - 59
D < 0 so nature of root is imaginary / non - real roots
More information about nature of root of quadratic equation
⇒ The discriminant of a quadratic equation ax² + bx +c = 0 is given b² - 4ac
The symbol Δ is sometimes used for discriminant
Note that the discriminant is the part of quadratic formula that is under the square root sign