Question

For what values of a quadratic equation 30ax2 – 6x + 1 = 0 has no real roots?

Answer 1

Answer:
For values of 'a' greater than 3/10, given quadratic equation will have no real roots.
Explanation:
KNOWLEDGE REQUIRED:
For a quadratic equation given in the from
a x² + b x + c = 0
The equation will have
Two distinct real roots when
Discriminant = b² - 4 ac > 0
Two equal real roots when
Discriminant = b² - 4 a c = 0
No real roots when
Discriminant = b² - 4 a c < 0
SOLUTION:
Given quadratic equation is 30 a x² - 6 x + 1 = 0
Since, when equation will have no real roots then, Discriminant of this equation will be less than zero
so,
→ Discriminant = (-6)² - 4 (30 a) (1) < 0
→ (-6)² - 4 (30 a) (1) < 0
→ 36 - 120 a < 0
→ 36 < 120 a
→ 120 a > 36
→ a > 36 / 120
→ a > 3 / 10
Therefore,
For values of 'a' greater than 3/10, given quadratic equation will have no real roots.

Answer 2

Step-by-step explanation:

there you go I hope u understand