Form a quadratic polynomial, the sum and product of whose zeroes are (−3) and 2 respectively.

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CBSE Class 10 Science – Chapter 2: Acids Form a quadratic polynomial In the experimental setup given below it is observed that on passing the gas produced in the reaction in the solution X Polynomial x^4 + 7x^3 + 7x^2 + px + q is exactly divisible by x^2 + 7x + 12

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Here’s a breakdown of the question in simple language, along with examples:

Understanding Zeroes:

  • Imagine a quadratic polynomial is a road that goes up and down, like a hill.
  • The “zeroes” are the points where the road crosses the x-axis, kind of like where the hill meets the ground.
  • The question is asking you to build a road (polynomial) that has its “hills” hitting the ground at specific points (zeroes) that have a particular relationship to each other.

Sum and Product of Zeroes:

  • The “sum” of the zeroes is what you get when you add them together.
  • The “product” of the zeroes is what you get when you multiply them.
  • The question gives you these clues about the zeroes: their sum is -3 and their product is 2.

Building the Polynomial:

  • To build the polynomial, we use a special pattern: x² – (sum of zeroes)x + (product of zeroes)
  • Plugging in the values from the question, we get: x² – (-3)x + 2
  • Simplifying, we get the quadratic polynomial: x² + 3x + 2

Example with Numbers:

  • Imagine the zeroes are -1 and -2.
  • Their sum is -1 + (-2) = -3.
  • Their product is (-1) x (-2) = 2.
  • The polynomial would be x² + 3x + 2.

Key Points:

  • The zeroes of a quadratic polynomial are the values of x that make the polynomial equal to zero.
  • The sum and product of the zeroes can be found using the coefficients of the polynomial.
  • The coefficient of x² is always 1.
  • The coefficient of x is the negative of the sum of the zeroes.
  • The constant term is the product of the zeroes.

Also Check out other Questions…

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