Formation of a Quadratic Equation From It's Roots

Q. If the zeroes of the polynomial $x^2+px+q$ are double in value to the zeroes of $2x^2-5x–3$, find the value of 𝒑 and 𝒒.

Q.

Write a quadratic polynomial, the sum and product of whose zeroes are $3$ and$-2$ respectively.

Q.

What is the relation between zeroes and coefficients of the given quadratic polynomial?

Q. Find the zeroes of the quadratic polynomial $x^2-3x-28$ and verify the relationship between the zeros and the coefficients.

Q. For the quadratic equation : $9x^2+4x+15$ = 0, product of the roots = .

1. $\frac{5}{3}$
2. -$\frac{5}{3}$
3. $\frac{15}{4}$
4. $\frac{4}{15}$

Q.

Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are -

1. 1, 3

2. –1, 3

3. –1, –3

4. 1, –1

Q.

If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation can be:

1. $x^2–5x+10=0$

2. $x^2+5x–5=0$

3. $x^2–5x+5=0$

4. $x^2+10x+5=0$

Q.

Let $\alpha \ne \beta$, ${\alpha }^2+3=5\alpha$ and ${\beta }^2=5\beta -3$. The quadratic equation whose roots are $\frac{\alpha }{\beta }$ and $\frac{\beta }{\alpha }$ will be:

1. $3x^2-19x+3=0$

2. $3x^2+19x+3=0$

3. $3x^2-19x-3=0$

4. $3x^2-3x+1=0$

Q. The graph of the equation $3x^2+4x+5$ = 0 intersects the x-axis at point(s).

1. 0
2. 1
3. 2
4. 3

Q. The points at which the graph of a quadratic polynomial touch the $X$-axis are called the roots of the polynomial.

1. True
2. False