Question

For what value(s) of ‘a’ quadratic equation 30ax ^2 − 6x + 1 = 0 has no real
roots?
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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

GivEn :-

• A quadratic Equation + 30ax² − 6x + 1 = 0

To FinD :-

• To Find the discriminant and find the Solution.

CalculaTioN :-

To Find the discriminant of the Quadratic Equation.

30ax² - 6x + 1 = 0

Discriminant

$\sf{ {( - 6)}^{2} }{} - 4(30a)(1) < 0 \\ \\ {( - 6)}^{2} - 4(30a)(1) < 0 \\ \\ \sf{36 - 120a < 0}{} \\ \\ \sf{36 \ < 120a}{} \\ \\ 36 < 120a \\ \\ \sf{120a > 36}{} \\ \\ \sf{a > \frac{36}{120} }{} \\ \\ a > \frac{3}{10}$

Hence for a value of 'a' greater than 3/10 given quadratic Equation have no teal roots

More To KnoW :-

For a Given quadratic Equation.

• Two distinct Real roots

★ Discriminant b²-4ac > 0

• Two equal Real roots.

★ Discriminant b²- 4ac = 0

• No Real Roots

★ Discriminant b²- 4ac < 0