In how many places does the graph of the equation y = ax^2 + bx + c in

y=ax^2+bx+c will intersect x-axis twice, if b^2-4ac>0
y=ax^2+bx+c will intersect x-axis once, if b^2-4ac=0
y=ax^2+bx+c will not intersect x-axis, if b^2-4ac<0

(1) ac=4
We don't know value of b. Thus, we cannot deduce how many times y=ax^2+bx+c intersects x-axis.
NOT SUFFICIENT

(2) b=5
We don't know value of a*c. Thus, we cannot deduce how many times y=ax^2+bx+c intersects x-axis.
NOT SUFFICIENT

(1)+(2) b^2-4ac = 5^2 - 4*4 = 9 >0
We can deduce that y=ax^2+bx+c intersects x-axis twice.
SUFFICIENT

FINAL ANSWER IS (C)

Find the discriminant
b^2-4ac>0: 2 solutions
b^2-4ac=0: 1 solutions
b^2-4ac<0: 1 solutions

(1) insufic
(2) insufic

√b=√5
√b≥0, so b≥0
b=5

(1/2) insufic

b^2-4ac
5^2-4(4)=25-16=9>0
2 solutions

Ans (C)

In how many places does the graph of the equation \(y=ax^2+bx+c\) intersect the x - axis?

(1) ac = 4
For \(y=ax^2+bx+c\)
Discriminant = \(b^2 - 4ac\) which determines how many solution are there for the equation.
As nothing about b is given then discriminant is unknown. So we can't find the solution.

INSUFFICIENT.

(2) √b = √5
b = 5 nothing else.

INSUFFICIENT.

Together 1 and 2
We know for quadratic equations like \(ax^2+bx+c\), \(b^2−4ac\) is called the discriminant

The points where the curve intersects with the x-axis are the solutions of the curve.
Discriminant helps us find all such points.

If \(b^2 − 4ac > 0\) curve will intersect x-axis at two points
If \(b^2 − 4ac = 0\) curve will intersect x-axis at one point
If \(b^2 − 4ac < 0\) curve will not intersect x-axis.

Here case I is applicable since \(b^2 − 4ac = 9\) i.e. 2 points.

SUFFICIENT.

Answer C.

To find at how many places the graph intersects x axis,we need the value of discriminate b^2 - 4ac.
Now, from 1) we know 4ac = 16. Three cases are possible: if b^2 > 16, the discriminant will be positive, in that case the equation has 2 solutions and it will intersect x axis at 2 points. But if b^2 < 16, the equation will have no real solutions and hence no x intercept. Again, if b^2 = 4ac , the equation will have just one solution. Insufficient

2) We don't know anything about the value of a and c. Insufficient.

Together, the discriminant can be determined. Sufficient.

C is the answer.

y=ax^2+bx+c

discernment is 0 = no solution = not touches x axis
discernment is + ve = 2 solutions = touches x axis at 2 points
discernment is - ve = no solution = not touches x axis

Discrimant value = b^2- 4ac

(1) ac=4........then b^2-16......
if b=4...then D=0
if b>=4 then D>0
if b<4 then D<0

so without D value we cannot the no.of points of intersection of y and x-axis

INSUFFICIENT

(2) √b=√5

same as above without the values of c.....its INSUFFICIENT


Combing both we can get the value of D=+ve.....
so there are 2 points of intersection
SUFFICIENT

OA:C

Ans C

Check whether b^2 - 4ac is <0 or >0 or =0

(i)ac = 4 ..... then the discriminant depends on the values of b and the possible points at which the graph cuts x-axis can be 2,1 or 0. Not sufficient

(ii) b = 5 ..... then the discriminant depends on the values of a*c and the possible points at which the graph cuts x-axis can be 2,1 or 0. Not sufficient

Together b^2-4ac > 0 .... hence sufficnet

To decide how many roots, we need to know whether b^2 - 4acis positive, 0, or negative, we can figure it out only by combining statement 1 and 2. Therefore it is C

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