Answer:
Given, the quadratic equation is 2x² - √5x - 2 = 0.
We have to determine the roots of the quadratic equation.
By using the quadratic formula,
x = [-b ± √b² - 4ac]/2a
Here, a = 2, b = -√5 and c = -2
b² - 4ac = (-√5)² - 4(2)(-2)
= 5 + 16
= 21
So, x = [-(-√5) ± √21]/ 2(2)
= (√5 ± √21)/4
Therefore, the roots are (√5 + √21)/4 and (√5 - √21)/4.
✦ Try This: Find the roots of the quadratic equation x² + 5x - 2 = 0 using the quadratic formula
2x
2
+5x+5=0
This is of the form ax
+bx+c=0, where a=2,b=5,c=5
Therefore,
D=b
−4ac=25−40=−15<0
Therefore, the equation has no real roots.
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Verified answer
Answer:
Given, the quadratic equation is 2x² - √5x - 2 = 0.
We have to determine the roots of the quadratic equation.
By using the quadratic formula,
x = [-b ± √b² - 4ac]/2a
Here, a = 2, b = -√5 and c = -2
b² - 4ac = (-√5)² - 4(2)(-2)
= 5 + 16
= 21
So, x = [-(-√5) ± √21]/ 2(2)
= (√5 ± √21)/4
Therefore, the roots are (√5 + √21)/4 and (√5 - √21)/4.
✦ Try This: Find the roots of the quadratic equation x² + 5x - 2 = 0 using the quadratic formula
Answer:
2x
2
+5x+5=0
This is of the form ax
2
+bx+c=0, where a=2,b=5,c=5
Therefore,
D=b
2
−4ac=25−40=−15<0
Therefore, the equation has no real roots.