Use the discriminant to determine whether each quadratic equation has two unequa

Cem Hayes

Cem Hayes

Answered question

2021-09-29

Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution (a double root), or no real solution, without solving the equation.
25x220x+4=0

Answer & Explanation

Jozlyn

Jozlyn

Skilled2021-09-30Added 85 answers

Step 1
We know, for a quadratic equation of the form ax2+bx+c=0,(a0) the discriminant D is given by
D=b24ac, and depending on the nature of the discriminant the equation the nature of the roots
is identified as follows:
If D>0,Then given quadratic equation has two real and unequal roots.
If D<0,Then given quadratic equation has no real roots.
If D=0,Then given quadratic equation has a repeated real
root(a root with multiplicity 2).
Given equation is: 25x220x+4=0,a=25,b=20,c=4.
D=b24ac
D=(20)24(25)(4)
D=400400
D=0.
Hence given quadratic equation has a repeated real root
(a real root with multiplicity 2).
Step 2
Result:
Given quadratic equation has a single real root with multiplicity 2.

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