for what value of'a' quadratic equation 30ax^2
Answers
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
\begin{gathered}\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}\end{gathered}
(−6)
2
−4(30a)(1)<0
(−6)
2
−4(30a)(1)<0
36−120a<0
36 <120a
36<120a
120a>36
a>
120
36
a>
10
3
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
