If the graph of a polynomial intersects the x -axis at only one point, can it be a quadratic polynomial?
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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively
Solution: (i)1/4, -1 Now formula of quadratic equation is x²-(Sum of root)x + (Product of root) = 0 Plug the value in formula we get x² –(1/4)x -1 = 0 Multiply by 4 to remove denominator...
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If α and β are zeroes of a quadratic polynomial p(x) = rx^2+4x+4, Find the values of “r” if: – α^2 + β^2 = 24.
Solution: From the given polynomial p(x), α + β = −4/r, and αβ = −4/r………. (1) Since,(α + β)2 = α2 + β2 + 2αβ Given, α2 + β2 = 24 and from equation (1). Therefore, (−4/r)2=24+(2×4)/r 16/r2=24+(2×4)/r 16 = 24 r2 + 8r 3r2 + r – 2 = 0 3r2 + 3r...
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What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis?
When the graph of a speed time graph is a straight line parallel to the time axis, the object is moving with constant speed.
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In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point
Let there be two such mid points C and D. Then from above theorem AC = 1 /2 AB and AD = 1 /2 AB ∴ AC = AD But this is possible only...
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Sound can travel through (a) gases only (b) solids only (c) liquids only (d) solids, liquids and gases
Correct Answer is: (d) Sound is transmitted by particles (atoms or molecules) in a solid, liquid or gas colliding with each other. It is a wave which is created by vibrating...
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If one zero of the quadratic polynomial x^2 - 5x -6 is 6 then find the other zero.
Let a,6 be the zeros of given polynomial. Then a+6=5 ⇒ a=-1.
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Can a quadratic polynomial x^2 +kx+k have equal zeros for some odd integer k >l?
No, for equal zeros, k =0,4 ⇒ k should be even.
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If the graph of a polynomial intersects the x-axis at exactly two points, is it necessarily a quadratic PolYnomial?
No, x4 - 1 is a polynomial intersecting the x-axis at exactly two points.
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Find the equation of the line which intersects the x-axis at a distance of 3 units to the left of origin with slope –2
It is known that if a line with slope m makes x-intercept d, then the equation of the line is given as y = m(x – d) For the line intersecting...
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There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi.
(d) Number of students who speak only English = (Number of students who speak English – Number of students who speak both Hindi and English) = 21 – 10 = 11 Number...
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