3x^2+2√5x-5=0 by completing square
Answers
Answer:
yes, the given equation has two real roots. The real roots are \frac{\sqrt{5}}{3}35 and -\sqrt{5}−5 .
Step-by-step explanation:
The given quadratic equation is
3x^2+2\sqrt{5}x-5=03x2+25x−5=0
The discriminant is
D=b^2-4acD=b2−4ac
D=(2\sqrt{5}}^2-4(3)(-5)=20+60=80 > 0
Since the value of discriminant is positive, therefore the given equation has two real roots.
x=\frac{-b\pm \sqrt{D}}{2a}x=2a−b±D
x=\frac{-2\sqrt{5}\pm \sqrt{80}}{2(3)}x=2(3)−25±80
x=\frac{-2\sqrt{5}\pm 4\sqrt{5}}{6}x=6−25±45
x=\frac{-2\sqrt{5}+4\sqrt{5}}{6},\frac{-2\sqrt{5}-4\sqrt{5}}{6}x=6−25+45,6−25−45
x=\frac{\sqrt{5}}{3},-\sqrt{5}
Step-by-step explanation:
((0 - 3x2) + 5x) - 5 = 0
3x2 + 5x - 5 = -1 • (3x2 - 5x + 5)
Factoring 3x2 - 5x + 5
The first term is, 3x2 its coefficient is 3 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 3 • 5 = 15
Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is -5 .
-15 + -1 = -16
-5 + -3 = -8
-3 + -5 = -8
-1 + -15 = -16
1 + 15 = 16
3 + 5 = 8
5 + 3 = 8
15 + 1 = 16