Question

please solve que no 9 and please give explanation​

Answer 1

• As we can see , the parabola is upside down ,

so , it directly implies to the value of 'a' that ,

=> a < 0 ........ (i)

since , a < 0

=> 2a < 0

now , -b/2a = x - coordinate of the vertex of parabola

• since, -b/2a lies to left of y-axis , we say

=> -b/2a < 0

[ ** multiplying both sides with a negative number , opposes the equality sign **

For example ,

• 2 < 3

• multiply by (-1) , => -2 > -3 ]

=> b/2a > 0

=> b < 0 ......... { since, 2a < 0 , so multiplying it on both sides , sign changes } ..........(ii)

and ,

=> f(x) = ax² + bx + c

=> f(0) = c

i.e. at x = 0 ; y = c

and from graph , c lies above x-axis , so ,

=> c > 0 ........ (iii)

So , the answer is ,

• a < 0

• b < 0

• c > 0