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If α and β are zeros of the polynomial p(x) =3x2-10x+7 then find the value of α3+β3 |
Answer» EXPLANATION.α and β are the zeroes of the polynomial. ⇒ 3x² - 10x + 7 = 0. As we KNOW that, Sum of the zeroes of the quadratic equation. ⇒ α + β = -b/a. ⇒ α + β = -(-10)/3 = 10/3. Products of the zeroes of the quadratic equation. ⇒ αβ = c/a. ⇒ αβ = 7/3. To find = (α³ + β³). As we know that, Formula of : ⇒ x³ + y³ = (x + y)(x² - xy + y²). ⇒ x² + y² = (x + y)² - 2xy. ⇒ (α³ + β³) = (α + β)(α² + β² - αβ). ⇒ (α³ + β³) = (α + β)[(α + β)² - 2αβ - αβ]. ⇒ (α³ + β³) = (α + β)[(α + β)² - 3αβ]. Put the values in the equation, we get. ⇒ (α³ + β³) = (10/3)[(10/3)² - 3(7/3)]. ⇒ (α³ + β³) = (10/3)[100/9 - 7]. ⇒ (α³ + β³) = (10/3)[100 - 63/9]. ⇒ (α³ + β³) = (10/3)[37/9]. ⇒ (α³ + β³) = 370/27. MORE INFORMATION.Nature of the FACTORS of the quadratic EXPRESSION.(1) = Real and different, if b² - 4ac > 0. (2) = Rational and different, if b² - 4ac is a perfect square. (3) = Real and equal, if b² - 4ac = 0. (4) = If D < 0 Roots are IMAGINARY and unequal or complex conjugate. |
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