Find the value of x in the polynomial 2x^2 + 5x - 3, given that it has a root at x = 1.

Q: Find the value of x in the polynomial 2x^2 + 5x - 3, given that it has a root at x = 1.

Step 1: Factorize the polynomial\nSince we know that x = 1 is a root of the polynomial, we can factorize the polynomial as: 2x^2 + 5x - 3 = (x - 1)(2x + 3) Step 2: Use the factor theorem\nBy the factor theorem, we know that if (x - a) is a factor of a polynomial, then a is a root of the polynomial. In this case, we have: (x - 1)(2x + 3) = 0\nThis implies that either (x - 1) = 0 or (2x + 3) = 0 Step 3: Solve for x\nSolving for x, we get:\nx - 1 = 0 --> x = 1 2x + 3 = 0 --> 2x = -3 --> x = -3/2 Conclusion\nTherefore, the value of x in the polynomial 2x^2 + 5x - 3 is x = -3/2.

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Accepted Answer

Step 1: Factorize the polynomial
Since we know that x = 1 is a root of the polynomial, we can factorize the polynomial as: 2x^2 + 5x - 3 = (x - 1)(2x + 3) Step 2: Use the factor theorem
By the factor theorem, we know that if (x - a) is a factor of a polynomial, then a is a root of the polynomial. In this case, we have: (x - 1)(2x + 3) = 0
This implies that either (x - 1) = 0 or (2x + 3) = 0 Step 3: Solve for x
Solving for x, we get:
x - 1 = 0 --> x = 1 2x + 3 = 0 --> 2x = -3 --> x = -3/2 Conclusion
Therefore, the value of x in the polynomial 2x^2 + 5x - 3 is x = -3/2.

CBSE · Class 10 · Mathematics · PolynomialsFind the value of x in the polynomial 2x^2 + 5x - 3, given that it has a root at x = 1.

Step 1: Factorize the polynomial\nSince we know that x = 1 is a root of the polynomial, we can factorize the polynomial as:

Step 2: Use the factor theorem\nBy the factor theorem, we know that if (x - a) is a factor of a polynomial, then a is a root of the polynomial. In this case, we have:

Step 3: Solve for x\nSolving for x, we get:\nx - 1 = 0 --> x = 1

Conclusion\nTherefore, the value of x in the polynomial 2x^2 + 5x - 3 is x = -3/2.