Class 10 Maths – Polynomials Quiz

If one zero of the polynomial \(p(x) = 6x^{2} + 37x - (k - 2)\) is the reciprocal of the other, then the value of \(k\) is:

For which value of \(k\) are the zeroes of the polynomial \(3x^{2} - 10x + k\) the reciprocals of each other?

If \(\alpha\) and \(\beta\) are the zeroes of the quadratic polynomial \(x^{2} - 8x + k\) such that \(\alpha^{2} + \beta^{2} = 40\), then the value of \(k\) is:

The number of polynomials having zeroes \(-3\) and \(4\) is:

If the sum of the zeroes of the quadratic polynomial \(kx^{2} + 2x + 3k\) is equal to their product, then \(k\) equals:

If one zero of the quadratic polynomial \(x^{2} + 3x + k\) is 2, then the value of \(k\) is:

If the product of the zeroes of the polynomial \(ax^{2} - 6x - 6\) is 4, then the value of \(a\) is:

For a non-zero polynomial \(ax^{2} + bx + c\) (with \(a \neq 0\), \(c \neq 0\)), the quadratic polynomial whose zeroes are the reciprocals of the zeroes of \(ax^{2} + bx + c\) is:

A quadratic polynomial whose sum of zeroes is \(-1\) and product of zeroes is \(-20\) is:

The graph of \(y = p(x)\) is given below for a polynomial \(p(x)\). The number of zeroes of \(p(x)\) is:

In the given figure, the graph of a polynomial \(f(x)\) is shown. The number of zeroes of the polynomial \(f(x)\) is:

What number should be added to the polynomial \(x^{2} - 5x + 4\), so that 3 is the zero of the resulting polynomial?

If the sum of the zeroes of the polynomial \(p(x) = (k^{2} - 14)x^{2} - 2x - 12\) is 1, then the value of \(k\) is:

If the sum of the zeroes of the quadratic polynomial \(3x^{2} - kx + 6\) is 3, then the value of \(k\) is:

The graph of a quadratic polynomial \(p(x)\) is drawn below. The number of real zeroes of \(p(x)\) is:

The area of a rectangular field is \((x^{2} + 3x - 10)\) square units. If the length of the field is \((x + 5)\) units, then the breadth of the field is:

If \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(p(x) = x^{2} - 5x + 6\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is:

A quadratic polynomial whose zeroes are \(3 + \sqrt{5}\) and \(3 - \sqrt{5}\) is:

If \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(x^{2} - 2x - 8\) with \(\alpha > \beta\), then the value of \(\alpha^{2} - \beta^{2}\) is:

For a quadratic polynomial \(p(x) = ax^{2} + bx + c\) with \(a \neq 0\), it is given that \(b = a + c\). Then which of the following is always a zero of \(p(x)\)?