Question

what value of p 3x square -2x+p square-4=0 one root be 0​

Answer 1

Answer :

p = ±2

Step-by-step explanation :

➤ Quadratic Polynomials :

✯ It is a polynomial of degree 2

✯ General form :

         ax² + bx + c  = 0

✯ Determinant, D = b² - 4ac

✯ Based on the value of Determinant, we can define the nature of roots.

       D > 0 ; real and unequal roots

       D = 0 ; real and equal roots

       D < 0 ; no real roots i.e., imaginary

✯ Relationship between zeroes and coefficients :

        ✩ Sum of zeroes = -b/a

         ✩ Product of zeroes = c/a

________________________________

Given,

• quadratic equation,

          3x² - 2x + p² - 4 = 0

• One root = 0

Since, 0 is a root;

substitute x = 0, the result is zero.

Put x = 0,

3(0)² - 2(0) + p² - 4 = 0

 3(0) - 0 + p² - 4 = 0

  0 - 0 + p² - 4 = 0

   p² - 4 = 0

    p² = 4

    p = √4

    p = ±2

Therefore, p = +2 , -2