📗 Chapter 2: Polynomials
- A quadratic polynomial p(x) = $$ax^2 + bx + c$$ has a < 0. The graph of this polynomial will be: (a) Upward Parabola (b) Downward Parabola (c) A Straight Line (d) A Circle
- If the zeroes of the quadratic polynomial $$ax^2 + bx + c$$, c is not equal to 0, then: (a) c and a have opposite signs (b) c and b have opposite signs (c) c and a have the same sign (d) c and b have the same sign
- Â Find the zeroes of the polynomial P(x) = $$3x^2 + 5x – 2$$Â and verify the relationship between the zeroes and its coefficients.
- If α and β are the zeroes of the polynomial $$2x^2 – 4x + 5$$, form a quadratic polynomial whose zeroes are $$\frac{1}{\alpha^2}$$ and $$\frac{1}{\beta^2}$$.
- The arch of a bridge is modeled by a quadratic polynomial p(x) = $$-x^2 + 6x – 5$$, where x is the horizontal distance in meters.
(i)Find the points where the arch meets the ground (zeroes of the polynomial).
(ii) What is the maximum height of the arch above the ground?
6. If one zero of p(x) = $$kx^2 + 4x + 4$$ is -2, find k.
7. Find the zeroes of $$3x^2 – x – 4$$ and verify the relationship with coefficients.
8. If one zero of the polynomial $$(a^2 + 9)x^2 + 13x + 6a$$ is the reciprocal of the other, find the value of a.
9. Case Study.
- A ball is thrown in the air, and its height h (in meters) after t seconds is given by h(t) = $$-5t^2 + 20t$$.
- What is the height of the ball at t = 1Â second?
- After how many seconds does the ball hit the ground? (Find the zeroes of the polynomial).
4. What is the maximum height reached by the ball?
10. If α and β are zeroes of the polynomial $$x^2 – 5x + 4$$, form a quadratic polynomial whose zeroes are $$\frac{1}{\alpha}$$ and $$\frac{1}{\beta}$$.