Question

Without determining the roots,comment on nature of roots of following equations
25x^2+20x+4=0​

Answer 1

Answer:

Roots are real and equal

Step-by-step explanation:

By finding the discriminant, We can find the nature of roots

Discriminant=b2-4ac (Here b2 means b square)

In the given equation

a=25,b=20,c=4

(20)square-4×25×4

=400-400

=0

Nature of the roots: Roots are real and equal

I hope this answer may help you

Answer 2

Step-by-step explanation:

Step by step solution :

STEP 1 :

Equation at the end of step 1

((0 - 52x2) + 20x) - 4 = 0

STEP 2 :

Pulling out like terms

3.1 Pull out like factors :

-25x2 + 20x - 4 = -1 • (25x2 - 20x + 4)

Trying to factor by splitting the middle term

3.2 Factoring 25x2 - 20x + 4

The first term is, 25x2 its coefficient is 25 .

The middle term is, -20x its coefficient is -20 .

The last term, "the constant", is +4

Step-1 : Multiply the coefficient of the first term by the constant 25 • 4 = 100

Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -20 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -10

25x2 - 10x - 10x - 4

Step-4 : Add up the first 2 terms, pulling out like factors :

5x • (5x-2)

Add up the last 2 terms, pulling out common factors :

2 • (5x-2)

Step-5 : Add up the four terms of step 4 :

(5x-2) • (5x-2)

Which is the desired factorization