Mathematics
Irrational numbers and real numbers
अपरिमेय संख्याएँ और वास्तविक संख्याएँ
In this Class 10 Mathematics topic, students build a clear understanding of real numbers as the collection of rational and irrational numbers. They learn to identify irrational numbers, compare and represent real numbers on the number line, and interpret terminating, recurring, and non-terminating non-recurring decimals. The topic also develops confidence with properties and operations involving real numbers, providing useful foundations for reading polynomial expressions, coefficients, and real zeros in the surrounding Polynomials chapter.
Practice questions
If (p(x)=2x^2-4x-1), which is the correct form of its zeroes?HardLevel 27Which pair can be irrational zeroes of a quadratic polynomial with rational coefficients?HardLevel 27If (p(x)=x^2-2\sqrt{3}x+3), which statement about its zeroes is correct?HardLevel 27If (\alpha=\sqrt{5}) and (\beta=-\sqrt{5}), which is the correct pair of (\alpha+\beta) and (\alpha\beta)?HardLevel 27Which polynomial has zeros \\(1+\sqrt{10}\\) and \\(1-\sqrt{10}\\)?HardLevel 27If (p(x)=3x^2-12x+6), what are its zeroes?HardLevel 27If (p(x)=x^2+4x+1), what are the sum and type of its zeroes?HardLevel 27If the zeroes are (\frac{1+\sqrt{3}}{2}) and (\frac{1-\sqrt{3}}{2}), what is their product?HardLevel 27For which value of \(k\) will the zeroes of \(x^2-2x+k\) be real and irrational?HardLevel 27If (p(x)=x^2-8x+7), how do its zeroes compare with those of (x^2-8x+10)?HardLevel 27If (a+\sqrt{b}) and (a-\sqrt{b}) are zeroes of a monic quadratic polynomial, what is the constant term?HardLevel 27Which polynomial has real zeroes but not rational zeroes?HardLevel 27If (\sqrt{2}) and (\sqrt{3}) are zeroes of a quadratic polynomial, what type of coefficients will that polynomial have?HardLevel 27If (p(x)=x^2-(2+\sqrt{3})x+\sqrt{3}), what are its zeroes?HardLevel 27If (p(x)=x^2-(1+\sqrt{3})x+\sqrt{3}), what are its zeroes?HardLevel 27If (p(x)=x^2-2x-2), what is the value of (p(\sqrt{2}))?HardLevel 27If (p(\sqrt{3})=0) and (p(x)=x^2+ax+3), what is the value of (a)?HardLevel 27If (p(x)=x^2-5), where will the graph (y=p(x)) cut the (x)-axis?HardLevel 27For which values of p and q will \(x^2+px+q\) have zeros \(4+\sqrt{7}\) and \(4-\sqrt{7}\)?HardLevel 27If (p(x)=x^2-4x-6), which is the correct pair of zeroes?HardLevel 27