Math, asked by kutarvirajita, 4 months ago

For what value(s) of 'a' quadratic equation 30 ax2 - 6x +1 = 0 has no real
roots?​

Answers

Answered by amansharma264
12

EXPLANATION.

quadratic equation = 30ax² - 6x + 1 = 0.

Equation has no real roots.

[ D < 0 Or b² - 4ac < 0 ].

→ (-6)² - 4(30a)(1) < 0.

→ 36 - 120a < 0.

→ 36 > 120a

→ 36/120 > a.

→ 3/10 > a.

More information.

(1) = D = 0 [ b² - 4ac = 0 ]

Roots are real and equal.

(2) = D < 0 [ b² - 4ac < 0 ]

Roots are imaginary.

(3) = D > 0 [ b² - 4ac > 0 ]

Roots are real and unequal.

Answered by Anonymous
40

Question :-

For what value of 'a' , quadratic equation 30ax² - 6x + 1 = 0 has no real roots?

Answer :-

If the quadratic equation has no real roots, then the value of discriminant (D) is less than 0.

Here,

  • a = 30a
  • b = -6
  • c = 1

\sf D = b^2-2ac

\sf D = (-6)^2 - 2 \times 30a \times 1 &lt; 0

\sf 36 - 60a &lt; 0

\sf 36 &lt; 60a

\sf a &gt; \frac{60}{36}

\sf a &gt; \frac{5}{3}

\boxed{\sf Value \:of \:a = \big( \frac{5}{3} , \infty \big) }

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