Find the number of real zeros of the following polynomial: $p(x) = x^{2} - 2x$.
- A$2$
- B$0$
- C$1$
- D$4$
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If the product of the zeros of $p(x) = ax^{2} - 6x - 6$ is $4$,then $a = $ ............
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View SolutionAnswer the following and justify:
Can the quadratic polynomial $x^{2}+kx+k$ have equal zeroes for some odd integer $k > 1$?
Can the quadratic polynomial $x^{2}+kx+k$ have equal zeroes for some odd integer $k > 1$?
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View SolutionFind the number of real zeros of the polynomial $y = p(x)$ from the given figure.
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View SolutionWhich of the following groups matches the data of Part $I$ with the data of Part $II$?
Part $I$ Part $II$ $1.$ The graph of $p(x)=x^{2}-5x+6$ $a.$ Intersects the $X$-axis at one point. $2.$ The graph of $p(x)=x^{2}-10x+25$ $b.$ Intersects the $X$-axis at zero points. $3.$ The graph of $p(x)=x^{3}-4x$ $c.$ Intersects the $X$-axis at two points. $4.$ The graph of $p(x)=x^{2}+4x+5$ $d.$ Intersects the $X$-axis at three points.
| Part $I$ | Part $II$ |
| $1.$ The graph of $p(x)=x^{2}-5x+6$ | $a.$ Intersects the $X$-axis at one point. |
| $2.$ The graph of $p(x)=x^{2}-10x+25$ | $b.$ Intersects the $X$-axis at zero points. |
| $3.$ The graph of $p(x)=x^{3}-4x$ | $c.$ Intersects the $X$-axis at two points. |
| $4.$ The graph of $p(x)=x^{2}+4x+5$ | $d.$ Intersects the $X$-axis at three points. |
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View SolutionIf the zero of the polynomial $p(x) = ax^2 - 11x + 3$ is $1$,then $a = \ldots$
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