Maths-
General
Easy
Question
If a, b and c are three consecutive positive terms of a G.P. then the graph of y = ax2 + bx + c is
- a curve that intersects the x-axis at two distinct points.
- entirely below the x-axis.
- entirely above the x-axis.
- tangent to the x-axis.
Hint:
calculate the discriminant and deduce the property of the graph.
The correct answer is: entirely above the x-axis.
entirely above x axis
Discriminant of the equation y = ax2 + bx + c :
D = b2 – 4 ac = a2 r2 -4(a)(ar2 ) = a2 r2 - 4a2 r2 = -3 a2 r2 , which is less than 0.
We know that when D < 0, roots are imaginary or complex and the graph lies above the x axis in this case since the value of a >0.
Nature of graph of a quadratic equation is given by its discriminant.
Here, a = a, b= ar, c = ar2 , where r is the common ratio of the GP
Given, a,b,c>0
Related Questions to study
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If ln (a + c) , ln (c – a), ln (a – 2b + c) are in A.P., then :
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An = A1+(n-1)x d
A2= A1 + d
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If ln (a + c) , ln (c – a), ln (a – 2b + c) are in A.P., then :
Maths-General
an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements
An = A1+(n-1)x d
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A3 = A2+d
A3-A2=A2-A1
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