# Nature of Solutions Graphically

## Trending Questions

**Q.**

The slope of a line parallel to X-axis is

**Q.**

A polynomial y=f(x) when represented on graph cuts x−axis at 2 points and y−axis at 3 points. What is the number of zeroes of f(x) ?

- 0
- 3
- 5
- 2

**Q.**

**Polynomials in Real Life**

**Polynomials are everywhere. It is found in a roller coaster of an amusement park, the slope of a hill, the curve of a bridge or the continuity of a mountain range. They play a key role in the study of algebra, in analysis and on the whole many mathematical problems involving them.**

**Based on the given information, answer the following question:
If the path traced by the Roller Coaster is represented by the graph y=p(x), find the number of zeroes?**

- 0
- 1
- 2
- 3

**Q.**Question 5

Classify the following as linear, quadriatic and cubic polynomials:

(i) x2+x

(ii) x−x3

(iii) y+y2+4

(iv) 1 + x

(v) 3t

(vi) r2

(viii)7x3

**Q.**Graph of quadratic function is

- circle
- parabola
- triangle
- rectangle

**Q.**The graph of the equation 3x2+4x+5 = 0 intersects the x-axis at

- \N
- 1
- 2
- 3

**Q.**Which of the following graph represents y=−x2?

**Q.**

Draw the graph of y=x2−4x+6 and show that it does not have real roots.

**Q.**

If logax>y and 0<a<1 . Then

x>y

x>ay

x=ay

x<ay

**Q.**Choose the option having correct match regarding the shape of the parabola for the polynomial ax2+bx+c.

I. If a > 0, then it is opening upward.

ii. If a > 0, then it is opening downward.

iii. If a < 0, then it is opening upward.

iv. If a < 0, then it is opening downward.

- I and III
- I and IV
- II and IV
- II and III

**Q.**Draw a graph for the polynomial p(x)=x2+3x−4 and find its zeroes from the graph.

**Q.**

The roots of a quadratic equation x2−4x−log3a=0 are real. Then what is the least value of a?

64

181

164

81

**Q.**The quadratic expression (2x+1)2−px+q≠0 for any real x if

- p2−16p−8q<0
- p2−8p+16q<0
- p2−8p−16q<0
- p2−16p+8q<0

**Q.**lf x∈R and the roots of ax2+bx+c=0 are non-real complex, then the sign of a2x2+abx+ac is

- always non-negative
- always zero
- always positive
- always negative

**Q.**The graph of a quadratic polynomial y=px2−qx+r is as shown in the adjacent figure, then

- p+q>0
- r2−4q<0
- r2−4p<0
- r−p−q>0

**Q.**If a>0 and b2−4ac>0, then the graph of y=ax2+bx+c

- lies entirely above the x-axis.
- is concave upwards and cuts the x-axis.
- touches the x-axis and lies below it.
- is concave downwards.

**Q.**The graph of y=x2+3x+4

- lies entirely below the x-axis.
- lies entirely above the x-axis.
- cuts the x-axis.
- touches the x-axis and lies below it.

**Q.**If b2−4ac=0 then the graph of y=ax2+bx+c

- touches the x-axis.
- lies entirely above the x-axis.
- cuts x-axis in two real points.
- can not be determined.

**Q.**

**Polynomials in Real Life**

**Polynomials are everywhere. It is found in a roller coaster of an amusement park, the slope of a hill, the curve of a bridge or the continuity of a mountain range. They play a key role in the study of algebra, in analysis and on the whole many mathematical problems involving them.**

**Based on the given information, answer the following question:
If the path traced by the Roller Coaster is represented by the graph y=p(x), find the number of zeroes?**

- 0
- 1
- 2
- 3

**Q.**Draw the graph of y=12x3−4x2−3x+1. Hence find the number of positive zeroes.

**Q.**Let f(x) be a quadratic expression which is positive for all real x. If g(x)=f(x)+f′(x)+f′′(x), then for any real x

- g(x)<0
- g(x)>0
- g(x)=0
- g(x)≥0

**Q.**If x2−x+a−3<0 for atleast one negative value of x, then complete set of values of a is

**Q.**If the LCM of pq and p3q is expressible in the form of (pq)k, then find the value of k.

- p3
- p
- p2

**Q.**For a triangle ABC it is given that cos A+cos B+cos C=32 Prove that the triangle is equilateral

- True
- False

**Q.**If b>a, then the equation (x−a)(x−b)−1=0 has

- both roots in [a, b]
- both roots in (−∞, a)
- both roots in (b, ∞)
- one root in (−∞, a) and other in (b, ∞)

**Q.**The given figure shows the graph of f(x)=ax2+bx+c, then

- ac<0
- abc<0
- bc>0
- ab>0

**Q.**If the LCM of pq and p3q is expressible in the form of (pq)k, then find the value of k.

- p3
- p
- p2

**Q.**The adjoining figure shows the graph of y=ax2+bx+c. Then

- a>0
- c>0
- b>0
- b2<4ac

**Q.**Assertion :STATEMENT-I : The curve y=−x22+x+1 is symmetric with respect to the line x=1. Reason: STATEMENT -2 : A parabola is symmetric about its axis.

- Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1
- Statement -1 is True, Statement -2 is true; Statement-2 is NOT a correct explanation for Statement-1
- Statement -1 is True, Statement -2 is False
- Statement -1 is False, Statement -2 is True

**Q.**For all x∈R, x2+2ax+(10−3a)>0. then the interval in which a lies is

- a<−5
- −5<a<2
- a>5
- 2<a<5