Question

. Identify the nature of roots of the given equation x2 + 5x - 12 = 0.
A. no real roots
B. real, rational and equal
C. real, irrational and unequal
D. real, rational and unequal.​

Answer 1

Answer:

real , rational and equal

Step-by-step explanation:

there is two power of x so it is real , rational and equal

Answer 2

Answer:

The nature of the root of the quadratic equation $x^{2} +5x-12=0$ are real, unequal, and rational

Step-by-step explanation:

• A quadratic equation has degree two, it can be represented as

                            $ax^{2} +bx+c=0$

• the  root or the value of x that satisfies the quadratic equation is given by the formula

                 $x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}$     or $x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

From the question, we have given a quadratic equation of the form

$x^{2} +5x-12=0$

compare with the standard equation

⇒

$a=1\\b=5\\c=-12$

substitute these values to get the roots

$x=\frac{-5+\sqrt{25-4*(-12)} }{2} =1.75\\x=\frac{-5-\sqrt{25-4*(-12)} }{2} =-6.7$

that is the roots are real, unequal, and rational