Question

(3) Find the discriminant of 2x + 10x + 21 = 0​

Answer 1

Required Solution-

★ It is given that we have to find the value of the discriminant of the quadratic equation ${\red{\sf{2x + 10x + 21 = 0}}}$ and hence write the nature of the roots. A formula is given below, we have to use this formula to find the solution for this question.

${\small{\underline{\boxed{\sf{D \: = b^{2} - 4ac}}}}}$

Discriminant tell us about there are solution of a quadratic equation as no solution, one solution and two solutions.

Knowledge about Quadratic equations-

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

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~ To solve this question we just have to put the values according to the formula!

${\sf{:\implies 2x + 10x + 21 = 0}}$

${\sf{:\implies 12x + 21 = 0}}$

${\sf{:\implies D \: = b^{2} - 4ac}}$

${\sf{:\implies D \: = (12)^{2} -4(0)(21)}}$

${\sf{:\implies D \: = (12)^{2} -4(0)}}$

${\sf{:\implies D \: = (12)^{2} -4 \times 0}}$

${\sf{:\implies D \: = (12)^{2} - 0}}$

${\sf{:\implies D \: = 12 \times 12 - 0}}$

${\sf{:\implies D \: = 144 - 0}}$

${\sf{:\implies D \: = 144}}$

• Henceforth, the discriminant is 144 here. Henceforth, we have done. Question is solved!