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 (\sqrt{2}) and (-\sqrt{8}) are zeroes of a polynomial, what is the simplified form of their sum?ExpertLevel 25Which option correctly gives the zeroes of (x^2-2\sqrt{3}x-1)?ExpertLevel 25If (p(x)=x^2-(a+b)x+ab) and (a=\sqrt{2}), (b=\sqrt{18}), what is the product of the zeroes?ExpertLevel 25If (p(x)=x^2+4x+2), which is the correct pair of zeroes?ExpertLevel 25If (\alpha) and (\beta) are zeroes of (x^2-3x-2), what is ((\alpha-\beta)^2)?ExpertLevel 25If one zero of (p(x)=x^2-2kx+5) is (\sqrt{5}), what will be the other zero and (k)?ExpertLevel 25Under which condition will the zeroes of (x^2+bx+c) be real but not rational?ExpertLevel 25If (\alpha) and (\beta) are zeroes of (x^2-2x-11), what is (\alpha^2+\beta^2+\alpha\beta)?ExpertLevel 25If \(p(x)=x^2-(3+\sqrt{2})x+3\sqrt{2}\), which is the correct pair of zeroes?ExpertLevel 25If p(x)=x^2−16, which statement about the type of zeroes is correct?EasyLevel 25Which of the following polynomials has both zeroes as irrational real numbers?ExpertLevel 25If (p(x)=x^2+2\sqrt{7}x+6), what is the discriminant?ExpertLevel 25If (p(x)=x^2+2\sqrt{7}x+6), what are its zeroes?ExpertLevel 25If the zeroes of x²+px−3 are 2+√7 and 2−√7, what is p?MediumLevel 25If (p(x)=x^2-2x+n) has equal and irrational zeroes, which statement about (n) is correct?ExpertLevel 25If one zero of a quadratic polynomial with rational coefficients is (\frac{3+\sqrt{5}}{2}), what will be the other zero?ExpertLevel 25If the zeroes are \\(
\\frac{3+\\sqrt{5}}{2}
\\) and \\(
\\frac{3-\\sqrt{5}}{2}
\\), what is the monic quadratic polynomial?ExpertLevel 25If \(p(x)=x^2-2\sqrt{2}x+1\), what is the type of its zeroes?ExpertLevel 25If (p(x)=x^2-(\sqrt{2}+\sqrt{8})x+4), what is the sum of its zeroes?ExpertLevel 25If (p(x)=x^2-11x+24) and (q(x)=x^2-11x+23), which statement is correct?ExpertLevel 25