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.

$\large\underline{\pink{\sf \orange{\bigstar} Given:-}}$

• 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

$\large\underline{\green{\sf \orange{\bigstar} Solution:-}}$

• 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

$\large\underline{\blue{\sf \orange{\bigstar} So:-}}$

→ 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

$\large\underline{\red{\sf \orange{\bigstar} Therefore:-}}$,

• For values of 'a' greater than 3/10, given quadratic equation will have no real roots.