Question

What is the nature of root of the quadratic equation 3x^2-15x+90=0

Answer 1

Answer :-

To find the nature of the roots, we first need to find value of discriminant :-

→ D = b² - 4ac

For the given equation,

• a = 3
• b = -15
• c = 90

→ D = (-15)² - 4 × 90 × 3

→ D = 225 - 1080

→ D = - 855

Here, we got the value of discriminant as negative. So, the roots of the given quadratic equation are imaginary.

Additional information :-

Nature of the roots :-

1. If D > 0, then roots are real and different.

2. If D is a perfect square, then roots are rational and different.

3. If D = 0, then roots are real and equal.

4. If D < 0 then, roots are imaginary and unequal or complex conjugate.

Answer 2

$\huge\sf\mathbb\color{blue}\underline{\colorbox{white}{♥️AɴSᴡᴇʀ♥️}}$

$\bold\purple{ \: answer \: = \: - 31 \: }$

ɢɪᴠᴇɴ,

$2 {x}^{2} - 3x \: + 5 \: = \: 0$

ᴄᴏᴍᴘᴀʀɪɴɢ ᴡɪᴛʜ ᴛʜᴇ sᴛᴀɴᴅᴀʀᴅ ǫᴜᴀᴅʀᴀᴛɪᴄ ᴇǫᴜᴀᴛɪᴏɴ ɪs

$a {x}^{2} + bx + c$

⇢ ʜᴇʀᴇ

• ᴀ = 2
• ʙ = -3
• ᴄ = 5

ɴᴏᴡ ,

$d \: = {b}^{2} - 4ac$

=9−4×2×5

=−31

Here, the discriminant is negative.

Thus the quadratic question does not have any real roots.