Finding Constants Using Zeroes of a Quadratic Polynomial Video Explanation Question If the zeroes of the quadratic polynomial \[ f(x) = x^2 + (a + 1)x + b \] are \(2\) and \(-3\), find the values of \(a\) and \(b\). Options: (a) \(a = -7,\; b = -1\) (b) \(a = 5,\; b = -1\) […]
Nature of Zeroes of a Quadratic Polynomial Video Explanation Question The zeroes of the quadratic polynomial \[ f(x) = x^2 + 99x + 127 \] are: (a) both positive (b) both negative (c) both equal (d) one positive and one negative Solution Step 1: Use Relations Between Zeroes and Coefficients For a quadratic polynomial \[
The Zeroes of the Quadratic Polynomial x² + 99x + 127 Read More »
Finding the Value of k Using Zero of a Polynomial Video Explanation Question If one of the zeroes of the quadratic polynomial \[ f(x) = (k – 1)x^2 + kx + 1 \] is \(-3\), find the value of \(k\). Solution Step 1: Use the Zero Condition If \(-3\) is a zero of the polynomial,
Number of Polynomials Having Given Zeroes Video Explanation Question The number of polynomials having zeroes \( -2 \) and \( 5 \) is: Solution Step 1: Form a Polynomial with the Given Zeroes If a polynomial has zeroes \( -2 \) and \( 5 \), then \[ (x + 2)(x – 5) \] is a
The Number of Polynomials Having Zeroes −2 and 5 Read More »
Finding a Polynomial Using Division Algorithm Video Explanation Question The polynomial which when divided by \[ -x^2 + x – 1 \] gives quotient \[ x – 2 \] and remainder \[ 3 \] is: (a) \(x^3 – 3x^2 + 3x – 5\) (b) \(-x^3 – 3x^2 – 3x – 5\) (c) \(-x^3 + 3x^2
The Polynomial Which When Divided by −x² + x − 1 Gives Quotient x − 2 and Remainder 3 Read More »
Finding Constants Using Factor Theorem Video Explanation Question If \(x+2\) is a factor of the polynomial \[ f(x) = x^2 + ax + 2b \] and \[ a + b = 4, \] then find the values of \(a\) and \(b\). Options: (a) \(a = 1,\; b = 3\) (b) \(a = 3,\; b =
If x + 2 Is a Factor of x² + ax + 2b and a + b = 4, Find the Values of a and b Read More »
Finding the Third Zero of a Cubic Polynomial Video Explanation Question If two zeroes of the polynomial \[ f(x) = x^3 + 3x^2 – 5x – 15 \] are \( \sqrt{5} \) and \( -\sqrt{5} \), find its third zero. Options: (a) 3 (b) -3 (c) 5 (d) -5 Solution Step 1:
If √5 and −√5 Are Two Zeroes of the Polynomial x³ + 3x² − 5x − 15, Find Its Third Zero Read More »
Finding the Third Zero of a Cubic Polynomial Video Explanation Question If two zeroes of the polynomial \[ f(x) = x^3 + x^2 – 9x – 9 \] are \(3\) and \(-3\), find its third zero. Options: (a) -1 (b) 1 (c) -9 (d) 9 Solution Step 1: Use the Formula for
If Two Zeroes of the Polynomial x³ + x² − 9x − 9 Are 3 and −3, Find Its Third Zero Read More »
Finding a Quadratic Polynomial from Given Zeroes Video Explanation Question A quadratic polynomial, the sum of whose zeroes is \(0\) and one zero is \(3\), is: (a) \(x^2 – 9\) (b) \(x^2 + 9\) (c) \(x^2 + 3\) (d) \(x^2 – 3\) Solution Step 1: Find the Other Zero Let the zeroes
A Quadratic Polynomial Whose Sum of Zeroes Is 0 and One Zero Is 3 Read More »
Making a Given Number a Zero of a Polynomial Video Explanation Question What should be subtracted from the polynomial \[ f(x) = x^2 – 16x + 30 \] so that \(15\) is a zero of the resulting polynomial? Options: (a) 30 (b) 14 (c) 15 (d) 16 Solution Step 1: Use the