Question

determine the nature of the roots of following quadratic equation. 2x²+5x+15​

Answer 1

Answer:

the roots are not real .

Step-by-step explanation:

on comparing with the standard form of quadratic equation we get,

a=2. b=5 c=15

square of b -4×a×c=25-120

=-95

so when the root is negative its nature is not real.

please select my answer as brainly.

Answer 2

Question :

$\sf{2 {x}^{2} + 5x + 15}$

Solution :

$\sf{2 {x}^{2} + 5x + 15} \\ \sf{Comparing \: with \: a {x}^{2} + bx + c = 0, \: we \: get, \: } \\ \sf{a = 2, \: b = 5, \: c = 15}$

$\implies\sf{Δ = {b}^{2} - 4 \: a \: c} \: \: \: \: \: \: \: \: \: \: \: \\ \implies\sf{Δ = {5}^{2} - 4 \times 2 \times 15} \\ \implies\sf{Δ =25 - 8 \times 15} \: \: \: \: \: \: \: \\ \implies\sf{Δ = 25 - 120 } \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies\sf{Δ = - 95 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{As \: Δ < 0 ,} \\ \sf{ the \: roots \: of \: the \: quadratic \: equation} \\ \sf{ are \: not \: real}$

Know more :

• If Δ = 0 then the roots of the equation are real and equal.
• If Δ > 0 then the roots of the quadratic equation are real and unequal.
• If Δ < 0 then the roots of the quadratic equation are not real.