Question

write the nature of the root without solving the equation 2 x square minus 3 root 2 X + 9/4 =0​

Answer 1

The roots of the given quadratic equation are imaginary.

Step-by-step explanation:

If a quadratic equation is,

ax^2+bx+cax2+bx+c

Then,

D=b^2-4acD=b2−4ac is called the discriminant of the quadratic equation,

If D > 0, then, the quadratic equation has two distinct real roots,

If D < 0, then, the quadratic equation has two distinct imaginary roots,

If D = 0, then, the quadratic equation has two real equal roots,

Here, the given quadratic equation is,

2x^2-4x+32x2−4x+3

Since, (4)² - 4×2×3 = 16 - 24 = -8 < 0,

Hence, both roots of the given equation are imaginary.

Answer 2

ANS:

2x²-3root2x+9/4=0

LCM (next) 8x²-12root2x+9=0

a=8, b=-12root2, c=9

D=b²-4ac

=(-12root2)²-4×8×9

=288-148

=140

D=140

means D>1

hence roots are real & distinct exists.

Hope it helped u

Mark me as BRAINLIST .✌