Product of Remaining Zeroes of a Cubic Polynomial Video Explanation Question If one of the zeroes of the cubic polynomial \[ f(x) = x^3 + ax^2 + bx + c \] is \(-1\), find the product of the other two zeroes. Options: (a) \(b – a + 1\) (b) \(b – a – 1\) (c) […]
Nature of Zeroes of a Quadratic Polynomial Video Explanation Question The zeroes of the quadratic polynomial \[ f(x) = x^2 + ax + a,\quad a \neq 0 \] are: (a) cannot both be positive (b) cannot both be negative (c) are always unequal (d) are always equal Solution Step 1: Use Relations Between Zeroes and
The Zeroes of the Quadratic Polynomial x² + ax + a (a ≠ 0) Read More »
Product of Zeroes of a Cubic Polynomial Video Explanation Question Given that one of the zeroes of the cubic polynomial \[ f(x) = ax^3 + bx^2 + cx + d \] is zero, find the product of the other two zeroes. Solution Step 1: Write Relations Between Zeroes and Coefficients Let the zeroes of the
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 »